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

Theorem stdpc6 1954
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1955.) 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.)
Ref Expression
stdpc6 𝑥 𝑥 = 𝑥

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1936 . 2 𝑥 = 𝑥
21ax-gen 1719 1 𝑥 𝑥 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator