Theorem stdpc6 1126

Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1179.) 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	⊢ ∀x x = x

Proof of Theorem stdpc6

Step	Hyp	Ref	Expression
1		equid 1125	. 2 ⊢ x = x
2	1	ax-gen 962	1 ⊢ ∀x x = x

Syntax hints:  ∀wal 953   = wceq 955

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-12 967  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122

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