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Theorem stdpc6 1573
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1635.) 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.)
Assertion
Ref Expression
stdpc6 x x = x

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1571 . 2 x = x
21ax-gen 1318 1 x x = x
Colors of variables: wff set class
Syntax hints:  wal 1226
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1318  ax-ie2 1364  ax-8 1376  ax-17 1400  ax-i9 1404
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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