Theorem stdpc6 1636

Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1700.) 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

Step	Hyp	Ref	Expression
1		equid 1634	. 2 |- x = x
2	1	ax-gen 1383	1 |- A. x x = x

Syntax hints:   A.wal 1287

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-gen 1383  ax-ie2 1428  ax-8 1440  ax-17 1464  ax-i9 1468

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)