Theorem nf5-1 2012

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 1587	. . 3 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> E. x A. x ph ) )
2		hbe1a 2011	. . 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 2010	1 |- ( A. x ( ph -> A. x ph ) -> F/ x ph )

Syntax hints:   -> wi 4   A.wal 1341   F/wnf 1448   E.wex 1480

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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by:  nf5d  2013