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Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1917.) 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 | ⊢ ∀x x = x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1676 | . 2 ⊢ x = x | |
2 | 1 | ax-gen 1546 | 1 ⊢ ∀x x = x |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 |
This theorem depends on definitions: df-bi 177 df-ex 1542 |
This theorem is referenced by: cbv3h 1983 |
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