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Theorem stdpc6 1870
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1871.) 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 1855 . 2  |-  x  =  x
21ax-gen 1669 1  |-  A. x  x  =  x
Colors of variables: wff setvar class
Syntax hints:   A.wal 1442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851
This theorem depends on definitions:  df-bi 189  df-ex 1664
This theorem is referenced by: (None)
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