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Theorem stdpc6 1715
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1946.) 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

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1706 . 2
21ax-gen 1570 1
Colors of variables: wff set class
Syntax hints:  A.wal 1564
This theorem is referenced by:  cbv3hOLD  1984  cbv3hOLD11  31275
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1570  ax-4 1581  ax-5 1644  ax-6 1685  ax-7 1705
This theorem depends on definitions:  df-bi 179  df-ex 1566
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