Theorem nfbidfOLD 2201

Description: Obsolete proof of nfbidf 2092 as of 6-Oct-2021. (Contributed by Mario Carneiro, 4-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfbidfOLD.1	|- F/ x ph
nfbidfOLD.2	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
nfbidfOLD	|- ( ph -> ( F/ x ps <-> F/ x ch ) )

Proof of Theorem nfbidfOLD

Step	Hyp	Ref	Expression
1		nfbidfOLD.1	. . 3 |- F/ x ph
2		nfbidfOLD.2	. . . 4 |- ( ph -> ( ps <-> ch ) )
3	1, 2	albidOLD 2199	. . . 4 |- ( ph -> ( A. x ps <-> A. x ch ) )
4	2, 3	imbi12d 334	. . 3 |- ( ph -> ( ( ps -> A. x ps ) <-> ( ch -> A. x ch ) ) )
5	1, 4	albidOLD 2199	. 2 |- ( ph -> ( A. x ( ps -> A. x ps ) <-> A. x ( ch -> A. x ch ) ) )
6		df-nfOLD 1721	. 2 |- ( F/ x ps <-> A. x ( ps -> A. x ps ) )
7		df-nfOLD 1721	. 2 |- ( F/ x ch <-> A. x ( ch -> A. x ch ) )
8	5, 6, 7	3bitr4g 303	1 |- ( ph -> ( F/ x ps <-> F/ x ch ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   F/wnfOLD 1709

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-nfOLD 1721

This theorem is referenced by: (None)