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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
PART 4  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      4.1  Mathboxes for user contributions
      4.2  Mathbox for Mykola Mostovenko
      4.3  Mathbox for BJ
      4.4  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 532
            1.2.6  Logical disjunction   wo 616
            1.2.7  Stable propositions   wstab 727
            1.2.8  Testable propositions   wtest 730
            1.2.9  Decidable propositions   wdc 733
            *1.2.10  Theorems of decidable propositions   condc 740
            1.2.11  Miscellaneous theorems of propositional calculus   pm5.21nd 815
            1.2.12  Abbreviated conjunction and disjunction of three wff's   w3o 872
            1.2.13  True and false constants   wal 1226
                  *1.2.13.1  Universal quantifier for use by df-tru   wal 1226
                  *1.2.13.2  Equality predicate for use by df-tru   cv 1227
                  1.2.13.3  Define the true and false constants   wtru 1229
            1.2.14  Logical 'xor'   wxo 1251
            *1.2.15  Truth tables: Operations on true and false constants   truantru 1275
            *1.2.16  Stoic logic indemonstrables (Chrysippus of Soli)   mpto1 1297
            1.2.17  Auxiliary theorems for Alan Sare's virtual deduction tool, part 1   ee22 1301
      1.3  Predicate calculus mostly without distinct variables
            *1.3.1  Universal quantifier (continued)   ax-5 1316
            *1.3.2  Equality predicate (continued)   weq 1373
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1400
            1.3.4  Introduce Axiom of Existence   ax-i9 1404
            1.3.5  Additional intuitionistic axioms   ax-ial 1409
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1411
            1.3.7  The existential quantifier   19.8a 1464
            1.3.8  Equality theorems without distinct variables   a9e 1568
            1.3.9  Axioms ax-10 and ax-11   ax10o 1585
            1.3.10  Substitution (without distinct variables)   wsb 1627
            1.3.11  Theorems using axiom ax-11   equs5a 1657
      1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1674
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1685
            1.4.3  More theorems related to ax-11 and substitution   albidv 1687
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1720
            1.4.5  More substitution theorems   hbs1 1796
            1.4.6  Existential uniqueness   weu 1882
            *1.4.7  Aristotelian logic: Assertic syllogisms   barbara 1980
*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 2004
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2008
            2.1.3  Class form not-free predicate   wnfc 2147
            2.1.4  Negated equality and membership   wne 2186
                  2.1.4.1  Negated equality   neii 2190
                  2.1.4.2  Negated membership   neli 2277
            2.1.5  Restricted quantification   wral 2284
            2.1.6  The universal class   cvv 2535
            *2.1.7  Conditional equality (experimental)   wcdeq 2724
            2.1.8  Russell's Paradox   ru 2740
            2.1.9  Proper substitution of classes for sets   wsbc 2741
            2.1.10  Proper substitution of classes for sets into classes   csb 2829
            2.1.11  Define basic set operations and relations   cdif 2891
            2.1.12  Subclasses and subsets   df-ss 2908
            2.1.13  The difference, union, and intersection of two classes   difeq1 3032
                  2.1.13.1  The difference of two classes   difeq1 3032
                  2.1.13.2  The union of two classes   elun 3061
                  2.1.13.3  The intersection of two classes   elin 3103
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3144
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3180
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3194
            2.1.14  The empty set   c0 3201
            2.1.15  Conditional operator   cif 3310
            2.1.16  Power classes   cpw 3334
            2.1.17  Unordered and ordered pairs   csn 3350
            2.1.18  The union of a class   cuni 3554
            2.1.19  The intersection of a class   cint 3589
            2.1.20  Indexed union and intersection   ciun 3631
            2.1.21  Disjointness   wdisj 3719
            2.1.22  Binary relations   wbr 3738
            2.1.23  Ordered-pair class abstractions (class builders)   copab 3791
            2.1.24  Transitive classes   wtr 3828
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 3846
            2.2.2  Introduce the Axiom of Separation   ax-sep 3849
            2.2.3  Derive the Null Set Axiom   zfnuleu 3855
            2.2.4  Theorems requiring subset and intersection existence   nalset 3861
            2.2.5  Theorems requiring empty set existence   class2seteq 3890
            2.2.6  Collection principle   bnd 3899
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 3901
            2.3.2  Axiom of Pairing   ax-pr 3918
            2.3.3  Ordered pair theorem   opm 3945
            2.3.4  Ordered-pair class abstractions (cont.)   opabid 3968
            2.3.5  Power class of union and intersection   pwin 3993
            2.3.6  Epsilon and identity relations   cep 3998
            2.3.7  Partial and complete ordering   wpo 4005
            2.3.8  Set-like relations   wse 4038
            2.3.9  Ordinals   word 4048
      2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4120
            2.4.2  Ordinals (continued)   ordon 4162
      2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4201
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4204
            2.5.3  Transfinite induction   tfi 4232
      2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4238
            2.6.2  The natural numbers (i.e. finite ordinals)   com 4240
            2.6.3  Peano's postulates   peano1 4244
            2.6.4  Finite induction (for finite ordinals)   find 4249
            2.6.5  The Natural Numbers (continued)   nn0suc 4254
            2.6.6  Relations   cxp 4270
            2.6.7  Definite description binder (inverted iota)   cio 4792
            2.6.8  Functions   wfun 4823
            2.6.9  Restricted iota (description binder)   crio 5392
            2.6.10  Operations   co 5436
            2.6.11  "Maps to" notation   elmpt2cl 5621
            2.6.12  Function operation   cof 5633
            2.6.13  Functions (continued)   resfunexgALT 5660
            2.6.14  First and second members of an ordered pair   c1st 5688
            *2.6.15  Special "Maps to" operations   mpt2xopn0yelv 5776
            2.6.16  Function transposition   ctpos 5781
            2.6.17  Undefined values   pwuninel2 5819
            2.6.18  Functions on ordinals; strictly monotone ordinal functions   iunon 5821
            2.6.19  "Strong" transfinite recursion   crecs 5841
            2.6.20  Recursive definition generator   crdg 5877
            2.6.21  Finite recursion   cfrec 5897
            2.6.22  Ordinal arithmetic   c1o 5909
            2.6.23  Natural number arithmetic   nna0 5968
            2.6.24  Equivalence relations and classes   wer 6014
*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 6130
            3.1.2  Final derivation of real and complex number postulates   axcnex 6555
            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 6607
            3.2.2  Infinity and the extended real number system   cpnf 6658
            3.2.3  Restate the ordering postulates with extended real "less than"   axltirr 6687
            3.2.4  Ordering on reals   lttr 6692
            3.2.5  Initial properties of the complex numbers   mul12 6729
      3.3  Real and complex numbers - basic operations
            3.3.1  Addition   add12 6756
            3.3.2  Subtraction   cmin 6769
            3.3.3  Multiplication   kcnktkm1cn 6966
PART 4  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      4.1  Mathboxes for user contributions
            4.1.1  Mathbox guidelines   mathbox 7002
      4.2  Mathbox for Mykola Mostovenko
      4.3  Mathbox for BJ
            4.3.1  Propositional calculus   nnexmid 7004
            4.3.2  Predicate calculus   bj-ex 7009
            *4.3.3  Extensionality   bj-vtoclgft 7021
            *4.3.4  Bounded formulas   wbd 7039
            *4.3.5  Bounded classes   wbdc 7067
            *4.3.6  Bounded separation   ax-bdsep 7111
                  4.3.6.1  Delta_0-classical logic   ax-bj-d0cl 7147
                  4.3.6.2  Inductive classes and the class of natural numbers (finite ordinals)   wind 7149
                  *4.3.6.3  The first three Peano postulates   bj-peano2 7161
            *4.3.7  Axiom of infinity   ax-infvn 7163
                  *4.3.7.1  The set of natural numbers (finite ordinals)   ax-infvn 7163
                  *4.3.7.2  The remaining two Peano postulates   bdpeano5 7165
                  *4.3.7.3  Bounded induction   findset 7167
            *4.3.8  Set induction   setindft 7183
                  *4.3.8.1  Set induction   setindft 7183
                  *4.3.8.2  Full induction   bj-findis 7197
            *4.3.9  Strong collection   ax-strcoll 7200
            *4.3.10  Subset collection   ax-sscoll 7205
      4.4  Mathbox for David A. Wheeler
            *4.4.1  Allsome quantifier   walsi 7207

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