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Theorem stdpc6 1695
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1938.) 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 1684 . 2  |-  x  =  x
21ax-gen 1552 1  |-  A. x  x  =  x
Colors of variables: wff set class
Syntax hints:   A.wal 1546
This theorem is referenced by:  cbv3h  2036  cbv3hOLD7  29408
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683
This theorem depends on definitions:  df-bi 178  df-ex 1548
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