Theorem bj-axc11v

Description: Version of axc11 with a disjoint variable condition, which does not require ax-13 nor ax-10 . Remark: the following theorems ( hbae , nfae , hbnae , nfnae , hbnaes ) would need to be totally unbundled to be proved without ax-13 , hence would be simple consequences of ax-5 or nfv . (Contributed by BJ, 31-May-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axc11v	|- ( A. x x = y -> ( A. x ph -> A. y ph ) )

Proof

Step	Hyp	Ref	Expression
1		axc11rv	|- ( A. y y = x -> ( A. x ph -> A. y ph ) )
2	1	bj-aecomsv	|- ( A. x x = y -> ( A. x ph -> A. y ph ) )