MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  stdpc6 Unicode version

Theorem stdpc6 1821
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1891.) 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 1818 . 2  |-  x  =  x
21ax-gen 1536 1  |-  A. x  x  =  x
Colors of variables: wff set class
Syntax hints:   A.wal 1532
This theorem is referenced by:  cbv3ALT  1875
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-12o 1664  ax-9 1684  ax-4 1692
  Copyright terms: Public domain W3C validator