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Metamath Proof Explorer

Theorem bj-drnf2v

Description: Version of drnf2 with a disjoint variable condition, which does not require ax-10 , ax-11 , ax-12 , ax-13 . Instance of nfbidv . Note that the version of axc15 with a disjoint variable condition is actually ax12v2 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019) (Proof modification is discouraged.)

		Ref	Expression
	Hypothesis	bj-drnf2v.1	\|- ( A. x x = y -> ( ph <-> ps ) )
	Assertion	bj-drnf2v	\|- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-drnf2v.1	\|- ( A. x x = y -> ( ph <-> ps ) )
2	1	nfbidv	\|- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) )