Theorem bj-drnf2v 32751

Description: Version of drnf2 2330 with a dv condition, which does not require ax-13 2246. Could be labeled "nfbidv". Note that the version of axc15 2303 with a dv condition is actually ax12v2 2049 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-drnf2v.1	|- ( A. x x = y -> ( ph <-> ps ) )

Assertion

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

Distinct variable group:   x, y, z

Allowed substitution hints:   ph( x, y, z)   ps( x, y, z)

Proof of Theorem bj-drnf2v

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ z A. x x = y
2		bj-drnf2v.1	. 2 |- ( A. x x = y -> ( ph <-> ps ) )
3	1, 2	nfbidf 2092	1 |- ( A. x x = y -> ( F/ z ph <-> F/ z ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)