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Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1669.) Axiom 6 of [Mendelson] p. 95. Mendelson doesn't say why he prepended the redundant quantifier, but it was probably to be compatible with free logic (which is valid in the empty domain). (Contributed by NM, 16-Feb-2005.) |
Ref | Expression |
---|---|
stdpc6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1605 | . 2 | |
2 | 1 | ax-gen 1354 | 1 |
Colors of variables: wff set class |
Syntax hints: wal 1257 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 103 ax-gen 1354 ax-ie2 1399 ax-8 1411 ax-17 1435 ax-i9 1439 |
This theorem depends on definitions: df-bi 114 |
This theorem is referenced by: (None) |
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