Theorem ax11v 1307

Description: This is a version of ax-11o 1260 when the variables are distinct. Axiom (C8) of [Monk2] p. 105. See theorem ax11v2 1257 for the rederivation of ax-11o 1260 from this theorem.

Assertion

Ref	Expression
ax11v	|- (x = y -> (ph -> A.x(x = y -> ph)))

Distinct variable group:   x,y

Proof of Theorem ax11v

Step	Hyp	Ref	Expression
1		ax-16 1252	. . . 4 |- (A.x x = y -> ((x = y -> ph) -> A.x(x = y -> ph)))
2		ax-1 4	. . . 4 |- (ph -> (x = y -> ph))
3	1, 2	syl5 21	. . 3 |- (A.x x = y -> (ph -> A.x(x = y -> ph)))
4	3	a1d 12	. 2 |- (A.x x = y -> (x = y -> (ph -> A.x(x = y -> ph))))
5		ax-11o 1260	. 2 |- (-. A.x x = y -> (x = y -> (ph -> A.x(x = y -> ph))))
6	4, 5	pm2.61i 132	1 |- (x = y -> (ph -> A.x(x = y -> ph)))

Syntax hints:   -> wi 3  A.wal 995   = wceq 997

This theorem is referenced by:  sb56 1308

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-16 1252  ax-11o 1260

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