Theorem nfbiiOLD 1836

Description: Obsolete proof of nfbii 1778 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfbiiOLD.1	|- ( ph <-> ps )

Assertion

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

Proof of Theorem nfbiiOLD

Step	Hyp	Ref	Expression
1		nfbiiOLD.1	. . . 4 |- ( ph <-> ps )
2	1	albii 1747	. . . 4 |- ( A. x ph <-> A. x ps )
3	1, 2	imbi12i 340	. . 3 |- ( ( ph -> A. x ph ) <-> ( ps -> A. x ps ) )
4	3	albii 1747	. 2 |- ( A. x ( ph -> A. x ph ) <-> A. x ( ps -> A. x ps ) )
5		df-nfOLD 1721	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
6		df-nfOLD 1721	. 2 |- ( F/ x ps <-> A. x ( ps -> A. x ps ) )
7	4, 5, 6	3bitr4i 292	1 |- ( F/ x ph <-> F/ x ps )

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

This theorem depends on definitions:  df-bi 197  df-nfOLD 1721

This theorem is referenced by:  nfxfrOLD  1837  nfxfrdOLD  1838