Theorem nfan1OLD 2236

Description: Obsolete proof of nfan1 2068 as of 6-Oct-2021. (Contributed by Mario Carneiro, 3-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfan1OLD.1	|- F/ x ph
nfan1OLD.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfan1OLD	|- F/ x ( ph /\ ps )

Proof of Theorem nfan1OLD

Step	Hyp	Ref	Expression
1		nfan1OLD.2	. . . . 5 |- ( ph -> F/ x ps )
2	1	nfrdOLD 2190	. . . 4 |- ( ph -> ( ps -> A. x ps ) )
3	2	imdistani 726	. . 3 |- ( ( ph /\ ps ) -> ( ph /\ A. x ps ) )
4		nfan1OLD.1	. . . 4 |- F/ x ph
5	4	19.28OLD 2235	. . 3 |- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )
6	3, 5	sylibr 224	. 2 |- ( ( ph /\ ps ) -> A. x ( ph /\ ps ) )
7	6	nfiOLD 1734	1 |- F/ x ( ph /\ ps )

Syntax hints:   -> wi 4   /\ wa 384   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-an 386  df-ex 1705  df-nfOLD 1721

This theorem is referenced by:  nfanOLDOLD  2237