Theorem nfdvOLD 1873

Description: Obsolete proof of nf5dv 2025 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfdvOLD.1	|- ( ph -> ( ps -> A. x ps ) )

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem nfdvOLD

Step	Hyp	Ref	Expression
1		nfdvOLD.1	. . 3 |- ( ph -> ( ps -> A. x ps ) )
2	1	alrimiv 1855	. 2 |- ( ph -> A. x ( ps -> A. x ps ) )
3		df-nfOLD 1721	. 2 |- ( F/ x ps <-> A. x ( ps -> A. x ps ) )
4	2, 3	sylibr 224	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   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

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

This theorem is referenced by: (None)