Theorem stdpc6 1114

Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1163.) 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).

Assertion

Ref	Expression
stdpc6	|- A.x x = x

Proof of Theorem stdpc6

Step	Hyp	Ref	Expression
1		equid 1113	. 2 |- x = x
2	1	ax-gen 955	1 |- A.x x = x

Syntax hints:  A.wal 950   = wceq 1099

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-gen 955  ax-9 1102  ax-12 1104

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957

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