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Table of Contents Summary
PART 1  FIRST ORDER LOGIC WITH EQUALITY
      1.1  Pre-logic
      1.2  Propositional calculus
      1.3  Predicate calculus mostly without distinct variables
      1.4  Predicate calculus with distinct variables
PART 2  SET THEORY
      2.1  IZF Set Theory - start with the Axiom of Extensionality
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
      2.4  IZF Set Theory - add the Axiom of Union
      2.5  IZF Set Theory - add the Axiom of Set Induction
      2.6  IZF Set Theory - add the Axiom of Infinity
PART 3  REAL AND COMPLEX NUMBERS
      3.1  Construction and axiomatization of real and complex numbers
      3.2  Derive the basic properties from the field axioms
      3.3  Real and complex numbers - basic operations
      3.4  Integer sets
      3.5  Order sets
      3.6  Elementary real and complex functions
      3.7  Elementary limits and convergence
PART 4  ELEMENTARY NUMBER THEORY
      4.1  Elementary properties of divisibility
PART 5  GUIDES AND MISCELLANEA
      5.1  Guides (conventions, explanations, and examples)
PART 6  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      6.1  Mathboxes for user contributions
      6.2  Mathbox for Mykola Mostovenko
      6.3  Mathbox for BJ
      6.4  Mathbox for David A. Wheeler

Detailed Table of Contents
(* means the section header has a description)
PART 1  FIRST ORDER LOGIC WITH EQUALITY
      *1.1  Pre-logic
            *1.1.1  Inferences for assisting proof development   a1ii 1
      1.2  Propositional calculus
            1.2.1  Recursively define primitive wffs for propositional calculus   wn 3
            1.2.2  Propositional logic axioms for implication   ax-1 5
            *1.2.3  Logical implication   mp2b 8
            1.2.4  Logical conjunction and logical equivalence   wa 97
            1.2.5  Logical negation (intuitionistic)   ax-in1 544
            1.2.6  Logical disjunction   wo 629
            1.2.7  Stable propositions   wstab 739
            1.2.8  Decidable propositions   wdc 742
            *1.2.9  Theorems of decidable propositions   condc 749
            1.2.10  Testable propositions   dftest 822
            1.2.11  Miscellaneous theorems of propositional calculus   pm5.21nd 825
            1.2.12  Abbreviated conjunction and disjunction of three wff's   w3o 884
            1.2.13  True and false constants   wal 1241
                  *1.2.13.1  Universal quantifier for use by df-tru   wal 1241
                  *1.2.13.2  Equality predicate for use by df-tru   cv 1242
                  1.2.13.3  Define the true and false constants   wtru 1244
            1.2.14  Logical 'xor'   wxo 1266
            *1.2.15  Truth tables: Operations on true and false constants   truantru 1292
            *1.2.16  Stoic logic indemonstrables (Chrysippus of Soli)   mptnan 1314
            1.2.17  Logical implication (continued)   syl6an 1323
      1.3  Predicate calculus mostly without distinct variables
            *1.3.1  Universal quantifier (continued)   ax-5 1336
            *1.3.2  Equality predicate (continued)   weq 1392
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1419
            1.3.4  Introduce Axiom of Existence   ax-i9 1423
            1.3.5  Additional intuitionistic axioms   ax-ial 1427
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1429
            1.3.7  The existential quantifier   19.8a 1482
            1.3.8  Equality theorems without distinct variables   a9e 1586
            1.3.9  Axioms ax-10 and ax-11   ax10o 1603
            1.3.10  Substitution (without distinct variables)   wsb 1645
            1.3.11  Theorems using axiom ax-11   equs5a 1675
      1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1692
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1703
            1.4.3  More theorems related to ax-11 and substitution   albidv 1705
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1738
            1.4.5  More substitution theorems   hbs1 1814
            1.4.6  Existential uniqueness   weu 1900
            *1.4.7  Aristotelian logic: Assertic syllogisms   barbara 1998
*PART 2  SET THEORY
      2.1  IZF Set Theory - start with the Axiom of Extensionality
            2.1.1  Introduce the Axiom of Extensionality   ax-ext 2022
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2026
            2.1.3  Class form not-free predicate   wnfc 2165
            2.1.4  Negated equality and membership   wne 2204
                  2.1.4.1  Negated equality   neii 2208
                  2.1.4.2  Negated membership   neli 2296
            2.1.5  Restricted quantification   wral 2303
            2.1.6  The universal class   cvv 2554
            *2.1.7  Conditional equality (experimental)   wcdeq 2744
            2.1.8  Russell's Paradox   ru 2760
            2.1.9  Proper substitution of classes for sets   wsbc 2761
            2.1.10  Proper substitution of classes for sets into classes   csb 2849
            2.1.11  Define basic set operations and relations   cdif 2911
            2.1.12  Subclasses and subsets   df-ss 2928
            2.1.13  The difference, union, and intersection of two classes   difeq1 3052
                  2.1.13.1  The difference of two classes   difeq1 3052
                  2.1.13.2  The union of two classes   elun 3081
                  2.1.13.3  The intersection of two classes   elin 3123
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3164
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3200
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3214
            2.1.14  The empty set   c0 3221
            2.1.15  Conditional operator   cif 3328
            2.1.16  Power classes   cpw 3356
            2.1.17  Unordered and ordered pairs   csn 3372
            2.1.18  The union of a class   cuni 3577
            2.1.19  The intersection of a class   cint 3612
            2.1.20  Indexed union and intersection   ciun 3654
            2.1.21  Disjointness   wdisj 3742
            2.1.22  Binary relations   wbr 3761
            2.1.23  Ordered-pair class abstractions (class builders)   copab 3814
            2.1.24  Transitive classes   wtr 3851
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 3869
            2.2.2  Introduce the Axiom of Separation   ax-sep 3872
            2.2.3  Derive the Null Set Axiom   zfnuleu 3878
            2.2.4  Theorems requiring subset and intersection existence   nalset 3884
            2.2.5  Theorems requiring empty set existence   class2seteq 3913
            2.2.6  Collection principle   bnd 3922
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 3924
            2.3.2  Axiom of Pairing   ax-pr 3941
            2.3.3  Ordered pair theorem   opm 3968
            2.3.4  Ordered-pair class abstractions (cont.)   opabid 3991
            2.3.5  Power class of union and intersection   pwin 4016
            2.3.6  Epsilon and identity relations   cep 4021
            2.3.7  Partial and complete ordering   wpo 4028
            2.3.8  Founded and set-like relations   wfrfor 4061
            2.3.9  Ordinals   word 4086
      2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4157
            2.4.2  Ordinals (continued)   ordon 4199
      2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4244
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4247
            2.5.3  Transfinite induction   tfi 4283
      2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4289
            2.6.2  The natural numbers (i.e. finite ordinals)   com 4291
            2.6.3  Peano's postulates   peano1 4295
            2.6.4  Finite induction (for finite ordinals)   find 4300
            2.6.5  The Natural Numbers (continued)   nn0suc 4305
            2.6.6  Relations   cxp 4321
            2.6.7  Definite description binder (inverted iota)   cio 4843
            2.6.8  Functions   wfun 4874
            2.6.9  Restricted iota (description binder)   crio 5445
            2.6.10  Operations   co 5490
            2.6.11  "Maps to" notation   elmpt2cl 5676
            2.6.12  Function operation   cof 5688
            2.6.13  Functions (continued)   resfunexgALT 5715
            2.6.14  First and second members of an ordered pair   c1st 5743
            *2.6.15  Special "Maps to" operations   mpt2xopn0yelv 5832
            2.6.16  Function transposition   ctpos 5837
            2.6.17  Undefined values   pwuninel2 5875
            2.6.18  Functions on ordinals; strictly monotone ordinal functions   iunon 5877
            2.6.19  "Strong" transfinite recursion   crecs 5897
            2.6.20  Recursive definition generator   crdg 5934
            2.6.21  Finite recursion   cfrec 5955
            2.6.22  Ordinal arithmetic   c1o 5972
            2.6.23  Natural number arithmetic   nna0 6031
            2.6.24  Equivalence relations and classes   wer 6081
            2.6.25  Equinumerosity   cen 6197
            2.6.26  Pigeonhole Principle   phplem1 6293
            2.6.27  Finite sets   fidceq 6308
            2.6.28  Cardinal numbers   ccrd 6331
*PART 3  REAL AND COMPLEX NUMBERS
      3.1  Construction and axiomatization of real and complex numbers
            3.1.1  Dedekind-cut construction of real and complex numbers   cnpi 6342
            3.1.2  Final derivation of real and complex number postulates   axcnex 6907
            3.1.3  Real and complex number postulates restated as axioms   ax-cnex 6947
      3.2  Derive the basic properties from the field axioms
            3.2.1  Some deductions from the field axioms for complex numbers   cnex 6977
            3.2.2  Infinity and the extended real number system   cpnf 7028
            3.2.3  Restate the ordering postulates with extended real "less than"   axltirr 7057
            3.2.4  Ordering on reals   lttr 7063
            3.2.5  Initial properties of the complex numbers   mul12 7113
      3.3  Real and complex numbers - basic operations
            3.3.1  Addition   add12 7140
            3.3.2  Subtraction   cmin 7153
            3.3.3  Multiplication   kcnktkm1cn 7350
            3.3.4  Ordering on reals (cont.)   ltadd2 7386
            3.3.5  Real Apartness   creap 7532
            3.3.6  Complex Apartness   cap 7539
            3.3.7  Reciprocals   recextlem1 7599
            3.3.8  Division   cdiv 7618
            3.3.9  Ordering on reals (cont.)   ltp1 7777
            3.3.10  Imaginary and complex number properties   crap0 7877
      3.4  Integer sets
            3.4.1  Positive integers (as a subset of complex numbers)   cn 7881
            3.4.2  Principle of mathematical induction   nnind 7897
            *3.4.3  Decimal representation of numbers   c2 7931
            *3.4.4  Some properties of specific numbers   neg1cn 7987
            3.4.5  Simple number properties   halfcl 8115
            3.4.6  The Archimedean property   arch 8141
            3.4.7  Nonnegative integers (as a subset of complex numbers)   cn0 8144
            3.4.8  Integers (as a subset of complex numbers)   cz 8208
            3.4.9  Decimal arithmetic   cdc 8331
            3.4.10  Upper sets of integers   cuz 8436
            3.4.11  Rational numbers (as a subset of complex numbers)   cq 8517
            3.4.12  Complex numbers as pairs of reals   cnref1o 8544
      3.5  Order sets
            3.5.1  Positive reals (as a subset of complex numbers)   crp 8545
            3.5.2  Infinity and the extended real number system (cont.)   cxne 8644
            3.5.3  Real number intervals   cioo 8715
            3.5.4  Finite intervals of integers   cfz 8832
            *3.5.5  Finite intervals of nonnegative integers   elfz2nn0 8931
            3.5.6  Half-open integer ranges   cfzo 8957
            3.5.7  Miscellaneous theorems about integers   frec2uz0d 9054
            3.5.8  The infinite sequence builder "seq"   cseq 9080
            3.5.9  Integer powers   cexp 9123
      3.6  Elementary real and complex functions
            3.6.1  The "shift" operation   cshi 9284
            3.6.2  Real and imaginary parts; conjugate   ccj 9308
            3.6.3  Sequence convergence   caucvgrelemrec 9447
            3.6.4  Square root; absolute value   csqrt 9463
      3.7  Elementary limits and convergence
            3.7.1  Limits   cli 9667
            3.7.2  Finite and infinite sums   csu 9740
*PART 4  ELEMENTARY NUMBER THEORY
      4.1  Elementary properties of divisibility
            4.1.1  Rationality of square root of 2   sqr2irrlem 9745
            4.1.2  Algorithms   nn0seqcvgd 9748
PART 5  GUIDES AND MISCELLANEA
      5.1  Guides (conventions, explanations, and examples)
            *5.1.1  Conventions   conventions 9760
PART 6  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      6.1  Mathboxes for user contributions
            6.1.1  Mathbox guidelines   mathbox 9761
      6.2  Mathbox for Mykola Mostovenko
      6.3  Mathbox for BJ
            6.3.1  Propositional calculus   nnexmid 9763
            6.3.2  Predicate calculus   bj-ex 9766
            *6.3.3  Extensionality   bj-vtoclgft 9778
            *6.3.4  Bounded formulas   wbd 9796
            *6.3.5  Bounded classes   wbdc 9824
            *6.3.6  Bounded separation   ax-bdsep 9868
                  6.3.6.1  Delta_0-classical logic   ax-bj-d0cl 9908
                  6.3.6.2  Inductive classes and the class of natural numbers (finite ordinals)   wind 9914
                  *6.3.6.3  The first three Peano postulates   bj-peano2 9927
            *6.3.7  Axiom of infinity   ax-infvn 9930
                  *6.3.7.1  The set of natural numbers (finite ordinals)   ax-infvn 9930
                  *6.3.7.2  Peano's fifth postulate   bdpeano5 9932
                  *6.3.7.3  Bounded induction and Peano's fourth postulate   findset 9934
            *6.3.8  Set induction   setindft 9954
                  *6.3.8.1  Set induction   setindft 9954
                  *6.3.8.2  Full induction   bj-findis 9968
            *6.3.9  Strong collection   ax-strcoll 9971
            *6.3.10  Subset collection   ax-sscoll 9976
      6.4  Mathbox for David A. Wheeler
            *6.4.1  Allsome quantifier   walsi 9978

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