Theorem stdpc6 1800

Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1801.) 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 1791	. 2
2	1	ax-gen 1618	1

Syntax hints:  A.wal 1393

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790

This theorem depends on definitions:  df-bi 185  df-ex 1613