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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 529
            1.2.6  Logical disjunction   wo 613
            1.2.7  Stable propositions   wstab 723
            1.2.8  Decidable propositions   wdc 726
            *1.2.9  Theorems of decidable propositions   condc 733
            1.2.10  Testable propositions   dftest 806
            1.2.11  Miscellaneous theorems of propositional calculus   pm5.21nd 809
            1.2.12  Abbreviated conjunction and disjunction of three wff's   w3o 868
            1.2.13  True and false constants   wal 1224
                  *1.2.13.1  Universal quantifier for use by df-tru   wal 1224
                  *1.2.13.2  Equality predicate for use by df-tru   cv 1225
                  1.2.13.3  Define the true and false constants   wtru 1227
            1.2.14  Logical 'xor'   wxo 1249
            *1.2.15  Truth tables: Operations on true and false constants   truantru 1273
            *1.2.16  Stoic logic indemonstrables (Chrysippus of Soli)   mpto1 1295
            1.2.17  Logical implication (continued)   syl6an 1299
      1.3  Predicate calculus mostly without distinct variables
            *1.3.1  Universal quantifier (continued)   ax-5 1312
            *1.3.2  Equality predicate (continued)   weq 1368
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1395
            1.3.4  Introduce Axiom of Existence   ax-i9 1399
            1.3.5  Additional intuitionistic axioms   ax-ial 1403
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1405
            1.3.7  The existential quantifier   19.8a 1458
            1.3.8  Equality theorems without distinct variables   a9e 1562
            1.3.9  Axioms ax-10 and ax-11   ax10o 1579
            1.3.10  Substitution (without distinct variables)   wsb 1621
            1.3.11  Theorems using axiom ax-11   equs5a 1651
      1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1668
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1679
            1.4.3  More theorems related to ax-11 and substitution   albidv 1681
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1714
            1.4.5  More substitution theorems   hbs1 1790
            1.4.6  Existential uniqueness   weu 1876
            *1.4.7  Aristotelian logic: Assertic syllogisms   barbara 1974
*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 1998
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2002
            2.1.3  Class form not-free predicate   wnfc 2141
            2.1.4  Negated equality and membership   wne 2180
                  2.1.4.1  Negated equality   neii 2184
                  2.1.4.2  Negated membership   neli 2271
            2.1.5  Restricted quantification   wral 2278
            2.1.6  The universal class   cvv 2529
            *2.1.7  Conditional equality (experimental)   wcdeq 2718
            2.1.8  Russell's Paradox   ru 2734
            2.1.9  Proper substitution of classes for sets   wsbc 2735
            2.1.10  Proper substitution of classes for sets into classes   csb 2823
            2.1.11  Define basic set operations and relations   cdif 2885
            2.1.12  Subclasses and subsets   df-ss 2902
            2.1.13  The difference, union, and intersection of two classes   difeq1 3026
                  2.1.13.1  The difference of two classes   difeq1 3026
                  2.1.13.2  The union of two classes   elun 3055
                  2.1.13.3  The intersection of two classes   elin 3097
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3138
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3174
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3188
            2.1.14  The empty set   c0 3195
            2.1.15  Conditional operator   cif 3302
            2.1.16  Power classes   cpw 3326
            2.1.17  Unordered and ordered pairs   csn 3342
            2.1.18  The union of a class   cuni 3546
            2.1.19  The intersection of a class   cint 3581
            2.1.20  Indexed union and intersection   ciun 3623
            2.1.21  Disjointness   wdisj 3711
            2.1.22  Binary relations   wbr 3730
            2.1.23  Ordered-pair class abstractions (class builders)   copab 3783
            2.1.24  Transitive classes   wtr 3820
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 3838
            2.2.2  Introduce the Axiom of Separation   ax-sep 3841
            2.2.3  Derive the Null Set Axiom   zfnuleu 3847
            2.2.4  Theorems requiring subset and intersection existence   nalset 3853
            2.2.5  Theorems requiring empty set existence   class2seteq 3882
            2.2.6  Collection principle   bnd 3891
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 3893
            2.3.2  Axiom of Pairing   ax-pr 3910
            2.3.3  Ordered pair theorem   opm 3937
            2.3.4  Ordered-pair class abstractions (cont.)   opabid 3960
            2.3.5  Power class of union and intersection   pwin 3985
            2.3.6  Epsilon and identity relations   cep 3990
            2.3.7  Partial and complete ordering   wpo 3997
            2.3.8  Set-like relations   wse 4030
            2.3.9  Ordinals   word 4040
      2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4111
            2.4.2  Ordinals (continued)   ordon 4153
      2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4192
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4195
            2.5.3  Transfinite induction   tfi 4223
      2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4229
            2.6.2  The natural numbers (i.e. finite ordinals)   com 4231
            2.6.3  Peano's postulates   peano1 4235
            2.6.4  Finite induction (for finite ordinals)   find 4240
            2.6.5  The Natural Numbers (continued)   nn0suc 4245
            2.6.6  Relations   cxp 4261
            2.6.7  Definite description binder (inverted iota)   cio 4783
            2.6.8  Functions   wfun 4814
            2.6.9  Restricted iota (description binder)   crio 5383
            2.6.10  Operations   co 5427
            2.6.11  "Maps to" notation   elmpt2cl 5612
            2.6.12  Function operation   cof 5624
            2.6.13  Functions (continued)   resfunexgALT 5651
            2.6.14  First and second members of an ordered pair   c1st 5679
            *2.6.15  Special "Maps to" operations   mpt2xopn0yelv 5767
            2.6.16  Function transposition   ctpos 5772
            2.6.17  Undefined values   pwuninel2 5810
            2.6.18  Functions on ordinals; strictly monotone ordinal functions   iunon 5812
            2.6.19  "Strong" transfinite recursion   crecs 5832
            2.6.20  Recursive definition generator   crdg 5868
            2.6.21  Finite recursion   cfrec 5888
            2.6.22  Ordinal arithmetic   c1o 5900
            2.6.23  Natural number arithmetic   nna0 5959
            2.6.24  Equivalence relations and classes   wer 6005
*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 6121
            3.1.2  Final derivation of real and complex number postulates   axcnex 6553
            3.1.3  Real and complex number postulates restated as axioms   ax-cnex 6581
      3.2  Derive the basic properties from the field axioms
            3.2.1  Some deductions from the field axioms for complex numbers   cnex 6609
            3.2.2  Infinity and the extended real number system   cpnf 6660
            3.2.3  Restate the ordering postulates with extended real "less than"   axltirr 6689
            3.2.4  Ordering on reals   lttr 6695
            3.2.5  Initial properties of the complex numbers   mul12 6745
      3.3  Real and complex numbers - basic operations
            3.3.1  Addition   add12 6772
            3.3.2  Subtraction   cmin 6785
            3.3.3  Multiplication   kcnktkm1cn 6982
            3.3.4  Ordering on reals (cont.)   ltadd2 7018
            3.3.5  Real Apartness   creap 7164
            3.3.6  Complex Apartness   cap 7171
            3.3.7  Reciprocals   recextlem1 7220
            3.3.8  Division   cdiv 7239
            3.3.9  Ordering on reals (cont.)   ltp1 7396
            3.3.10  Imaginary and complex number properties   crap0 7496
      3.4  Integer sets
            3.4.1  Positive integers (as a subset of complex numbers)   cn 7500
            3.4.2  Principle of mathematical induction   nnind 7516
            *3.4.3  Decimal representation of numbers   c2 7549
            *3.4.4  Some properties of specific numbers   neg1cn 7605
            3.4.5  Simple number properties   halfcl 7732
            3.4.6  Nonnegative integers (as a subset of complex numbers)   cn0 7758
            3.4.7  Integers (as a subset of complex numbers)   cz 7822
            3.4.8  Decimal arithmetic   cdc 7935
            3.4.9  Rational numbers (as a subset of complex numbers)   cq 8040
      3.5  Order sets
            3.5.1  Positive reals (as a subset of complex numbers)   crp 8067
            3.5.2  Infinity and the extended real number system (cont.)   cxne 8165
            3.5.3  Real number intervals   cioo 8236
PART 4  GUIDES AND MISCELLANEA
      4.1  Guides (conventions, explanations, and examples)
            *4.1.1  Conventions   conventions 8353
PART 5  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      5.1  Mathboxes for user contributions
            5.1.1  Mathbox guidelines   mathbox 8354
      5.2  Mathbox for Mykola Mostovenko
      5.3  Mathbox for BJ
            5.3.1  Propositional calculus   nnexmid 8356
            5.3.2  Predicate calculus   bj-ex 8359
            *5.3.3  Extensionality   bj-vtoclgft 8371
            *5.3.4  Bounded formulas   wbd 8389
            *5.3.5  Bounded classes   wbdc 8417
            *5.3.6  Bounded separation   ax-bdsep 8461
                  5.3.6.1  Delta_0-classical logic   ax-bj-d0cl 8497
                  5.3.6.2  Inductive classes and the class of natural numbers (finite ordinals)   wind 8503
                  *5.3.6.3  The first three Peano postulates   bj-peano2 8515
            *5.3.7  Axiom of infinity   ax-infvn 8517
                  *5.3.7.1  The set of natural numbers (finite ordinals)   ax-infvn 8517
                  *5.3.7.2  The remaining two Peano postulates   bdpeano5 8519
                  *5.3.7.3  Bounded induction   findset 8521
            *5.3.8  Set induction   setindft 8537
                  *5.3.8.1  Set induction   setindft 8537
                  *5.3.8.2  Full induction   bj-findis 8551
            *5.3.9  Strong collection   ax-strcoll 8554
            *5.3.10  Subset collection   ax-sscoll 8559
      5.4  Mathbox for David A. Wheeler
            *5.4.1  Allsome quantifier   walsi 8561

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