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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 integer functions
      3.7  Elementary real and complex functions
      3.8  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
      6.5  Mathbox for Jim Kingdon

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 101
            1.2.5  Logical negation (intuitionistic)   ax-in1 554
            1.2.6  Logical disjunction   wo 639
            1.2.7  Stable propositions   wstab 750
            1.2.8  Decidable propositions   wdc 753
            *1.2.9  Theorems of decidable propositions   condc 760
            1.2.10  Testable propositions   dftest 833
            1.2.11  Miscellaneous theorems of propositional calculus   pm5.21nd 836
            1.2.12  Abbreviated conjunction and disjunction of three wff's   w3o 895
            1.2.13  True and false constants   wal 1257
                  *1.2.13.1  Universal quantifier for use by df-tru   wal 1257
                  *1.2.13.2  Equality predicate for use by df-tru   cv 1258
                  1.2.13.3  Define the true and false constants   wtru 1260
            1.2.14  Logical 'xor'   wxo 1282
            *1.2.15  Truth tables: Operations on true and false constants   truantru 1308
            *1.2.16  Stoic logic indemonstrables (Chrysippus of Soli)   mptnan 1330
            1.2.17  Logical implication (continued)   syl6an 1339
      1.3  Predicate calculus mostly without distinct variables
            *1.3.1  Universal quantifier (continued)   ax-5 1352
            *1.3.2  Equality predicate (continued)   weq 1408
            1.3.3  Axiom ax-17 - first use of the $d distinct variable statement   ax-17 1435
            1.3.4  Introduce Axiom of Existence   ax-i9 1439
            1.3.5  Additional intuitionistic axioms   ax-ial 1443
            1.3.6  Predicate calculus including ax-4, without distinct variables   spi 1445
            1.3.7  The existential quantifier   19.8a 1498
            1.3.8  Equality theorems without distinct variables   a9e 1602
            1.3.9  Axioms ax-10 and ax-11   ax10o 1619
            1.3.10  Substitution (without distinct variables)   wsb 1661
            1.3.11  Theorems using axiom ax-11   equs5a 1691
      1.4  Predicate calculus with distinct variables
            1.4.1  Derive the axiom of distinct variables ax-16   spimv 1708
            1.4.2  Derive the obsolete axiom of variable substitution ax-11o   ax11o 1719
            1.4.3  More theorems related to ax-11 and substitution   albidv 1721
            1.4.4  Predicate calculus with distinct variables (cont.)   ax16i 1754
            1.4.5  More substitution theorems   hbs1 1830
            1.4.6  Existential uniqueness   weu 1916
            *1.4.7  Aristotelian logic: Assertic syllogisms   barbara 2014
*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 2038
            2.1.2  Class abstractions (a.k.a. class builders)   cab 2042
            2.1.3  Class form not-free predicate   wnfc 2181
            2.1.4  Negated equality and membership   wne 2220
                  2.1.4.1  Negated equality   wne 2220
                  2.1.4.2  Negated membership   wnel 2314
            2.1.5  Restricted quantification   wral 2323
            2.1.6  The universal class   cvv 2574
            *2.1.7  Conditional equality (experimental)   wcdeq 2769
            2.1.8  Russell's Paradox   ru 2785
            2.1.9  Proper substitution of classes for sets   wsbc 2786
            2.1.10  Proper substitution of classes for sets into classes   csb 2879
            2.1.11  Define basic set operations and relations   cdif 2941
            2.1.12  Subclasses and subsets   df-ss 2958
            2.1.13  The difference, union, and intersection of two classes   difeq1 3082
                  2.1.13.1  The difference of two classes   difeq1 3082
                  2.1.13.2  The union of two classes   elun 3111
                  2.1.13.3  The intersection of two classes   elin 3153
                  2.1.13.4  Combinations of difference, union, and intersection of two classes   unabs 3194
                  2.1.13.5  Class abstractions with difference, union, and intersection of two classes   symdifxor 3230
                  2.1.13.6  Restricted uniqueness with difference, union, and intersection   reuss2 3244
            2.1.14  The empty set   c0 3251
            2.1.15  Conditional operator   cif 3358
            2.1.16  Power classes   cpw 3386
            2.1.17  Unordered and ordered pairs   csn 3402
            2.1.18  The union of a class   cuni 3607
            2.1.19  The intersection of a class   cint 3642
            2.1.20  Indexed union and intersection   ciun 3684
            2.1.21  Disjointness   wdisj 3772
            2.1.22  Binary relations   wbr 3791
            2.1.23  Ordered-pair class abstractions (class builders)   copab 3844
            2.1.24  Transitive classes   wtr 3881
      2.2  IZF Set Theory - add the Axioms of Collection and Separation
            2.2.1  Introduce the Axiom of Collection   ax-coll 3899
            2.2.2  Introduce the Axiom of Separation   ax-sep 3902
            2.2.3  Derive the Null Set Axiom   zfnuleu 3908
            2.2.4  Theorems requiring subset and intersection existence   nalset 3914
            2.2.5  Theorems requiring empty set existence   class2seteq 3943
            2.2.6  Collection principle   bnd 3952
      2.3  IZF Set Theory - add the Axioms of Power Sets and Pairing
            2.3.1  Introduce the Axiom of Power Sets   ax-pow 3954
            2.3.2  Axiom of Pairing   ax-pr 3971
            2.3.3  Ordered pair theorem   opm 3998
            2.3.4  Ordered-pair class abstractions (cont.)   opabid 4021
            2.3.5  Power class of union and intersection   pwin 4046
            2.3.6  Epsilon and identity relations   cep 4051
            2.3.7  Partial and complete ordering   wpo 4058
            2.3.8  Founded and set-like relations   wfrfor 4091
            2.3.9  Ordinals   word 4126
      2.4  IZF Set Theory - add the Axiom of Union
            2.4.1  Introduce the Axiom of Union   ax-un 4197
            2.4.2  Ordinals (continued)   ordon 4239
      2.5  IZF Set Theory - add the Axiom of Set Induction
            2.5.1  The ZF Axiom of Foundation would imply Excluded Middle   regexmidlemm 4284
            2.5.2  Introduce the Axiom of Set Induction   ax-setind 4289
            2.5.3  Transfinite induction   tfi 4332
      2.6  IZF Set Theory - add the Axiom of Infinity
            2.6.1  Introduce the Axiom of Infinity   ax-iinf 4338
            2.6.2  The natural numbers (i.e. finite ordinals)   com 4340
            2.6.3  Peano's postulates   peano1 4344
            2.6.4  Finite induction (for finite ordinals)   find 4349
            2.6.5  The Natural Numbers (continued)   nn0suc 4354
            2.6.6  Relations   cxp 4370
            2.6.7  Definite description binder (inverted iota)   cio 4892
            2.6.8  Functions   wfun 4923
            2.6.9  Restricted iota (description binder)   crio 5494
            2.6.10  Operations   co 5539
            2.6.11  "Maps to" notation   elmpt2cl 5725
            2.6.12  Function operation   cof 5737
            2.6.13  Functions (continued)   resfunexgALT 5764
            2.6.14  First and second members of an ordered pair   c1st 5792
            *2.6.15  Special "Maps to" operations   mpt2xopn0yelv 5884
            2.6.16  Function transposition   ctpos 5889
            2.6.17  Undefined values   pwuninel2 5927
            2.6.18  Functions on ordinals; strictly monotone ordinal functions   iunon 5929
            2.6.19  "Strong" transfinite recursion   crecs 5949
            2.6.20  Recursive definition generator   crdg 5986
            2.6.21  Finite recursion   cfrec 6007
            2.6.22  Ordinal arithmetic   c1o 6024
            2.6.23  Natural number arithmetic   nna0 6083
            2.6.24  Equivalence relations and classes   wer 6133
            2.6.25  Equinumerosity   cen 6249
            2.6.26  Pigeonhole Principle   phplem1 6345
            2.6.27  Finite sets   fidceq 6360
            2.6.28  Supremum and infimum   csup 6387
            2.6.29  Ordinal isomorphism   ordiso2 6414
            2.6.30  Cardinal numbers   ccrd 6416
*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 6427
            3.1.2  Final derivation of real and complex number postulates   axcnex 6992
            3.1.3  Real and complex number postulates restated as axioms   ax-cnex 7032
      3.2  Derive the basic properties from the field axioms
            3.2.1  Some deductions from the field axioms for complex numbers   cnex 7062
            3.2.2  Infinity and the extended real number system   cpnf 7115
            3.2.3  Restate the ordering postulates with extended real "less than"   axltirr 7144
            3.2.4  Ordering on reals   lttr 7150
            3.2.5  Initial properties of the complex numbers   mul12 7202
      3.3  Real and complex numbers - basic operations
            3.3.1  Addition   add12 7231
            3.3.2  Subtraction   cmin 7244
            3.3.3  Multiplication   kcnktkm1cn 7451
            3.3.4  Ordering on reals (cont.)   ltadd2 7487
            3.3.5  Real Apartness   creap 7638
            3.3.6  Complex Apartness   cap 7645
            3.3.7  Reciprocals   recextlem1 7705
            3.3.8  Division   cdiv 7724
            3.3.9  Ordering on reals (cont.)   ltp1 7884
            3.3.10  Imaginary and complex number properties   crap0 7985
      3.4  Integer sets
            3.4.1  Positive integers (as a subset of complex numbers)   cn 7989
            3.4.2  Principle of mathematical induction   nnind 8005
            *3.4.3  Decimal representation of numbers   c2 8039
            *3.4.4  Some properties of specific numbers   neg1cn 8094
            3.4.5  Simple number properties   halfcl 8207
            3.4.6  The Archimedean property   arch 8235
            3.4.7  Nonnegative integers (as a subset of complex numbers)   cn0 8238
            3.4.8  Integers (as a subset of complex numbers)   cz 8301
            3.4.9  Decimal arithmetic   cdc 8426
            3.4.10  Upper sets of integers   cuz 8568
            3.4.11  Rational numbers (as a subset of complex numbers)   cq 8650
            3.4.12  Complex numbers as pairs of reals   cnref1o 8679
      3.5  Order sets
            3.5.1  Positive reals (as a subset of complex numbers)   crp 8680
            3.5.2  Infinity and the extended real number system (cont.)   cxne 8786
            3.5.3  Real number intervals   cioo 8857
            3.5.4  Finite intervals of integers   cfz 8975
            *3.5.5  Finite intervals of nonnegative integers   elfz2nn0 9074
            3.5.6  Half-open integer ranges   cfzo 9100
            3.5.7  Rational numbers (cont.)   qtri3or 9199
      3.6  Elementary integer functions
            3.6.1  The floor and ceiling functions   cfl 9219
            3.6.2  The modulo (remainder) operation   cmo 9271
            3.6.3  Miscellaneous theorems about integers   frec2uz0d 9348
            3.6.4  The infinite sequence builder "seq"   cseq 9374
            3.6.5  Integer powers   cexp 9418
            3.6.6  Ordered pair theorem for nonnegative integers   nn0le2msqd 9586
            3.6.7  Factorial function   cfa 9592
            3.6.8  The binomial coefficient operation   cbc 9614
      3.7  Elementary real and complex functions
            3.7.1  The "shift" operation   cshi 9642
            3.7.2  Real and imaginary parts; conjugate   ccj 9666
            3.7.3  Sequence convergence   caucvgrelemrec 9805
            3.7.4  Square root; absolute value   csqrt 9822
      3.8  Elementary limits and convergence
            3.8.1  Limits   cli 10029
            3.8.2  Finite and infinite sums   csu 10102
*PART 4  ELEMENTARY NUMBER THEORY
      4.1  Elementary properties of divisibility
            4.1.1  The divides relation   cdvds 10107
            *4.1.2  Even and odd numbers   evenelz 10177
            4.1.3  Rationality of square root of 2   sqr2irrlem 10229
            4.1.4  Algorithms   nn0seqcvgd 10242
PART 5  GUIDES AND MISCELLANEA
      5.1  Guides (conventions, explanations, and examples)
            *5.1.1  Conventions   conventions 10254
            5.1.2  Definitional examples   ex-or 10255
PART 6  SUPPLEMENTARY MATERIAL (USER'S MATHBOXES)
      6.1  Mathboxes for user contributions
            6.1.1  Mathbox guidelines   mathbox 10263
      6.2  Mathbox for Mykola Mostovenko
      6.3  Mathbox for BJ
            6.3.1  Propositional calculus   nnexmid 10265
            6.3.2  Predicate calculus   bj-ex 10268
            *6.3.3  Extensionality   bj-vtoclgft 10280
            *6.3.4  Bounded formulas   wbd 10298
            *6.3.5  Bounded classes   wbdc 10326
            *6.3.6  Bounded separation   ax-bdsep 10370
                  6.3.6.1  Delta_0-classical logic   ax-bj-d0cl 10410
                  6.3.6.2  Inductive classes and the class of natural numbers (finite ordinals)   wind 10416
                  *6.3.6.3  The first three Peano postulates   bj-peano2 10429
            *6.3.7  Axiom of infinity   ax-infvn 10432
                  *6.3.7.1  The set of natural numbers (finite ordinals)   ax-infvn 10432
                  *6.3.7.2  Peano's fifth postulate   bdpeano5 10434
                  *6.3.7.3  Bounded induction and Peano's fourth postulate   findset 10436
            *6.3.8  Set induction   setindft 10456
                  *6.3.8.1  Set induction   setindft 10456
                  *6.3.8.2  Full induction   bj-findis 10470
            *6.3.9  Strong collection   ax-strcoll 10473
            *6.3.10  Subset collection   ax-sscoll 10478
            6.3.11  Real numbers   ax-ddkcomp 10480
      6.4  Mathbox for David A. Wheeler
            *6.4.1  Allsome quantifier   walsi 10481
      6.5  Mathbox for Jim Kingdon

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