ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  stdpc6 Unicode version

Theorem stdpc6 1607
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1669.) 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 1605 . 2  |-  x  =  x
21ax-gen 1354 1  |-  A. x  x  =  x
Colors of variables: wff set class
Syntax hints:   A.wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-gen 1354  ax-ie2 1399  ax-8 1411  ax-17 1435  ax-i9 1439
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator