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Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1801.) 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 1791 | . 2 | |
2 | 1 | ax-gen 1618 | 1 |
Colors of variables: wff setvar class |
Syntax hints: A. wal 1393 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 |
This theorem depends on definitions: df-bi 185 df-ex 1613 |
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