NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  stdpc6 Unicode version

Theorem stdpc6 1687
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1917.) 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

Proof of Theorem stdpc6
StepHypRef Expression
1 equid 1676 . 2
21ax-gen 1546 1
Colors of variables: wff setvar class
Syntax hints:  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  cbv3h  1983
  Copyright terms: Public domain W3C validator