Theorem stdpc6 1715

Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1946.) 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

Proof of Theorem stdpc6

Step	Hyp	Ref	Expression
1		equid 1706	. 2
2	1	ax-gen 1570	1

Syntax hints:  A.wal 1564

This theorem is referenced by:  cbv3hOLD  1984  cbv3hOLD11  31275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1570  ax-4 1581  ax-5 1644  ax-6 1685  ax-7 1705

This theorem depends on definitions:  df-bi 179  df-ex 1566