Theorem drnf2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Usage of this theorem is discouraged because it depends on ax-13 . Usage of nfbidv is preferred, which requires fewer axioms. (Contributed by Mario Carneiro, 4-Oct-2016) (Proof shortened by Wolf Lammen, 5-May-2018) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dral1.1	|- ( A. x x = y -> ( ph <-> ps ) )
Assertion	drnf2	|- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) )

Proof

Step	Hyp	Ref	Expression
1		dral1.1	|- ( A. x x = y -> ( ph <-> ps ) )
2		nfae	|- F/ z A. x x = y
3	2 1	nfbidf	|- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) )