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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
PART 4  GUIDES AND MISCELLANEA
      4.1  Guides (conventions, explanations, and examples)
PART 5  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      5.1  Mathboxes for user contributions
      5.2  Mathbox for Mykola Mostovenko
      5.3  Mathbox for BJ
      5.4  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   dummylink 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 628
            1.2.7  Stable propositions   wstab 738
            1.2.8  Decidable propositions   wdc 741
            *1.2.9  Theorems of decidable propositions   condc 748
            1.2.10  Testable propositions   dftest 821
            1.2.11  Miscellaneous theorems of propositional calculus   pm5.21nd 824
            1.2.12  Abbreviated conjunction and disjunction of three wff's   w3o 883
            1.2.13  True and false constants   wal 1240
                  *1.2.13.1  Universal quantifier for use by df-tru   wal 1240
                  *1.2.13.2  Equality predicate for use by df-tru   cv 1241
                  1.2.13.3  Define the true and false constants   wtru 1243
            1.2.14  Logical 'xor'   wxo 1265
            *1.2.15  Truth tables: Operations on true and false constants   truantru 1289
            *1.2.16  Stoic logic indemonstrables (Chrysippus of Soli)   mpto1 1311
            1.2.17  Logical implication (continued)   syl6an 1320
      1.3  Predicate calculus mostly without distinct variables
            *1.3.1  Universal quantifier (continued)   ax-5 1333
            *1.3.2  Equality predicate (continued)   weq 1389
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1416
            1.3.4  Introduce Axiom of Existence   ax-i9 1420
            1.3.5  Additional intuitionistic axioms   ax-ial 1424
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1426
            1.3.7  The existential quantifier   19.8a 1479
            1.3.8  Equality theorems without distinct variables   a9e 1583
            1.3.9  Axioms ax-10 and ax-11   ax10o 1600
            1.3.10  Substitution (without distinct variables)   wsb 1642
            1.3.11  Theorems using axiom ax-11   equs5a 1672
      1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1689
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1700
            1.4.3  More theorems related to ax-11 and substitution   albidv 1702
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1735
            1.4.5  More substitution theorems   hbs1 1811
            1.4.6  Existential uniqueness   weu 1897
            *1.4.7  Aristotelian logic: Assertic syllogisms   barbara 1995
*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 2019
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2023
            2.1.3  Class form not-free predicate   wnfc 2162
            2.1.4  Negated equality and membership   wne 2201
                  2.1.4.1  Negated equality   neii 2205
                  2.1.4.2  Negated membership   neli 2293
            2.1.5  Restricted quantification   wral 2300
            2.1.6  The universal class   cvv 2551
            *2.1.7  Conditional equality (experimental)   wcdeq 2741
            2.1.8  Russell's Paradox   ru 2757
            2.1.9  Proper substitution of classes for sets   wsbc 2758
            2.1.10  Proper substitution of classes for sets into classes   csb 2846
            2.1.11  Define basic set operations and relations   cdif 2908
            2.1.12  Subclasses and subsets   df-ss 2925
            2.1.13  The difference, union, and intersection of two classes   difeq1 3049
                  2.1.13.1  The difference of two classes   difeq1 3049
                  2.1.13.2  The union of two classes   elun 3078
                  2.1.13.3  The intersection of two classes   elin 3120
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3161
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3197
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3211
            2.1.14  The empty set   c0 3218
            2.1.15  Conditional operator   cif 3325
            2.1.16  Power classes   cpw 3350
            2.1.17  Unordered and ordered pairs   csn 3366
            2.1.18  The union of a class   cuni 3570
            2.1.19  The intersection of a class   cint 3605
            2.1.20  Indexed union and intersection   ciun 3647
            2.1.21  Disjointness   wdisj 3735
            2.1.22  Binary relations   wbr 3754
            2.1.23  Ordered-pair class abstractions (class builders)   copab 3807
            2.1.24  Transitive classes   wtr 3844
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 3862
            2.2.2  Introduce the Axiom of Separation   ax-sep 3865
            2.2.3  Derive the Null Set Axiom   zfnuleu 3871
            2.2.4  Theorems requiring subset and intersection existence   nalset 3877
            2.2.5  Theorems requiring empty set existence   class2seteq 3906
            2.2.6  Collection principle   bnd 3915
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 3917
            2.3.2  Axiom of Pairing   ax-pr 3934
            2.3.3  Ordered pair theorem   opm 3961
            2.3.4  Ordered-pair class abstractions (cont.)   opabid 3984
            2.3.5  Power class of union and intersection   pwin 4009
            2.3.6  Epsilon and identity relations   cep 4014
            2.3.7  Partial and complete ordering   wpo 4021
            2.3.8  Set-like relations   wse 4054
            2.3.9  Ordinals   word 4064
      2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4135
            2.4.2  Ordinals (continued)   ordon 4177
      2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4216
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4219
            2.5.3  Transfinite induction   tfi 4247
      2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4253
            2.6.2  The natural numbers (i.e. finite ordinals)   com 4255
            2.6.3  Peano's postulates   peano1 4259
            2.6.4  Finite induction (for finite ordinals)   find 4264
            2.6.5  The Natural Numbers (continued)   nn0suc 4269
            2.6.6  Relations   cxp 4285
            2.6.7  Definite description binder (inverted iota)   cio 4807
            2.6.8  Functions   wfun 4838
            2.6.9  Restricted iota (description binder)   crio 5408
            2.6.10  Operations   co 5452
            2.6.11  "Maps to" notation   elmpt2cl 5637
            2.6.12  Function operation   cof 5649
            2.6.13  Functions (continued)   resfunexgALT 5676
            2.6.14  First and second members of an ordered pair   c1st 5704
            *2.6.15  Special "Maps to" operations   mpt2xopn0yelv 5792
            2.6.16  Function transposition   ctpos 5797
            2.6.17  Undefined values   pwuninel2 5835
            2.6.18  Functions on ordinals; strictly monotone ordinal functions   iunon 5837
            2.6.19  "Strong" transfinite recursion   crecs 5857
            2.6.20  Recursive definition generator   crdg 5893
            2.6.21  Finite recursion   cfrec 5914
            2.6.22  Ordinal arithmetic   c1o 5926
            2.6.23  Natural number arithmetic   nna0 5985
            2.6.24  Equivalence relations and classes   wer 6032
            2.6.25  Equinumerosity   cen 6148
            2.6.26  Finite sets   nnfi 6244
*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 6249
            3.1.2  Final derivation of real and complex number postulates   axcnex 6697
            3.1.3  Real and complex number postulates restated as axioms   ax-cnex 6726
      3.2  Derive the basic properties from the field axioms
            3.2.1  Some deductions from the field axioms for complex numbers   cnex 6755
            3.2.2  Infinity and the extended real number system   cpnf 6806
            3.2.3  Restate the ordering postulates with extended real "less than"   axltirr 6835
            3.2.4  Ordering on reals   lttr 6841
            3.2.5  Initial properties of the complex numbers   mul12 6891
      3.3  Real and complex numbers - basic operations
            3.3.1  Addition   add12 6918
            3.3.2  Subtraction   cmin 6931
            3.3.3  Multiplication   kcnktkm1cn 7128
            3.3.4  Ordering on reals (cont.)   ltadd2 7164
            3.3.5  Real Apartness   creap 7310
            3.3.6  Complex Apartness   cap 7317
            3.3.7  Reciprocals   recextlem1 7366
            3.3.8  Division   cdiv 7385
            3.3.9  Ordering on reals (cont.)   ltp1 7542
            3.3.10  Imaginary and complex number properties   crap0 7642
      3.4  Integer sets
            3.4.1  Positive integers (as a subset of complex numbers)   cn 7646
            3.4.2  Principle of mathematical induction   nnind 7662
            *3.4.3  Decimal representation of numbers   c2 7695
            *3.4.4  Some properties of specific numbers   neg1cn 7751
            3.4.5  Simple number properties   halfcl 7878
            3.4.6  The Archimedean property   arch 7904
            3.4.7  Nonnegative integers (as a subset of complex numbers)   cn0 7907
            3.4.8  Integers (as a subset of complex numbers)   cz 7971
            3.4.9  Decimal arithmetic   cdc 8093
            3.4.10  Upper sets of integers   cuz 8198
            3.4.11  Rational numbers (as a subset of complex numbers)   cq 8279
      3.5  Order sets
            3.5.1  Positive reals (as a subset of complex numbers)   crp 8306
            3.5.2  Infinity and the extended real number system (cont.)   cxne 8404
            3.5.3  Real number intervals   cioo 8475
            3.5.4  Finite intervals of integers   cfz 8592
            *3.5.5  Finite intervals of nonnegative integers   elfz2nn0 8689
            3.5.6  Half-open integer ranges   cfzo 8715
            3.5.7  Miscellaneous theorems about integers   frec2uz0d 8812
PART 4  GUIDES AND MISCELLANEA
      4.1  Guides (conventions, explanations, and examples)
            *4.1.1  Conventions   conventions 8830
PART 5  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      5.1  Mathboxes for user contributions
            5.1.1  Mathbox guidelines   mathbox 8831
      5.2  Mathbox for Mykola Mostovenko
      5.3  Mathbox for BJ
            5.3.1  Propositional calculus   nnexmid 8833
            5.3.2  Predicate calculus   bj-ex 8836
            *5.3.3  Extensionality   bj-vtoclgft 8848
            *5.3.4  Bounded formulas   wbd 8866
            *5.3.5  Bounded classes   wbdc 8894
            *5.3.6  Bounded separation   ax-bdsep 8938
                  5.3.6.1  Delta_0-classical logic   ax-bj-d0cl 8974
                  5.3.6.2  Inductive classes and the class of natural numbers (finite ordinals)   wind 8980
                  *5.3.6.3  The first three Peano postulates   bj-peano2 8992
            *5.3.7  Axiom of infinity   ax-infvn 8994
                  *5.3.7.1  The set of natural numbers (finite ordinals)   ax-infvn 8994
                  *5.3.7.2  The remaining two Peano postulates   bdpeano5 8996
                  *5.3.7.3  Bounded induction   findset 8998
            *5.3.8  Set induction   setindft 9014
                  *5.3.8.1  Set induction   setindft 9014
                  *5.3.8.2  Full induction   bj-findis 9028
            *5.3.9  Strong collection   ax-strcoll 9031
            *5.3.10  Subset collection   ax-sscoll 9036
      5.4  Mathbox for David A. Wheeler
            *5.4.1  Allsome quantifier   walsi 9038

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