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Theorem stdpc6 1944
 Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1945.) 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 𝑥 𝑥 = 𝑥

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1926 . 2 𝑥 = 𝑥
21ax-gen 1713 1 𝑥 𝑥 = 𝑥
 Colors of variables: wff setvar class Syntax hints:  ∀wal 1473 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922 This theorem depends on definitions:  df-bi 196  df-ex 1696 This theorem is referenced by: (None)
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