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Theorem stdpc6 1651
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1859.) 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 1646 . 2  |-  x  =  x
21ax-gen 1534 1  |-  A. x  x  =  x
Colors of variables: wff set class
Syntax hints:   A.wal 1528
This theorem is referenced by:  cbv3h  1925
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645
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