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Theorem stdpc6 1670
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1870.) 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  |-  A. x  x  =  x

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1662 . 2  |-  x  =  x
21ax-gen 1536 1  |-  A. x  x  =  x
Colors of variables: wff set class
Syntax hints:   A.wal 1530
This theorem is referenced by:  cbv3h  1936  cbv3hwAUX7  29493  cbv3hOLD7  29678
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661
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