Theorem nf5-1 2004

Description: One direction of nf5 . (Contributed by Wolf Lammen, 16-Sep-2021.)

Assertion

Ref	Expression
nf5-1	|- ( A. x ( ph -> A. x ph ) -> F/ x ph )

Proof of Theorem nf5-1

Step	Hyp	Ref	Expression
1		exim 1579	. . 3 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> E. x A. x ph ) )
2		hbe1a 2003	. . 3 |- ( E. x A. x ph -> A. x ph )
3	1, 2	syl6 33	. 2 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> A. x ph ) )
4	3	nfd2 2002	1 |- ( A. x ( ph -> A. x ph ) -> F/ x ph )

Syntax hints:   -> wi 4   A.wal 1333   F/wnf 1440   E.wex 1472

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1441

This theorem is referenced by:  nf5d  2005