Theorem nfdhOLD 2194

Description: Obsolete proof of nf5dh 2026 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfdhOLD.1	|- ( ph -> A. x ph )
nfdhOLD.2	|- ( ph -> ( ps -> A. x ps ) )

Assertion

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

Proof of Theorem nfdhOLD

Step	Hyp	Ref	Expression
1		nfdhOLD.1	. . 3 |- ( ph -> A. x ph )
2	1	nfiOLD 1734	. 2 |- F/ x ph
3		nfdhOLD.2	. 2 |- ( ph -> ( ps -> A. x ps ) )
4	2, 3	nfdOLD 2193	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  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:  hbimdOLD  2230