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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
StepHypRef 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 )
31, 2syl6 33 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  A. x ph )
)
43nfd2 2002 1  |-  ( A. x ( ph  ->  A. x ph )  ->  F/ x ph )
Colors of variables: wff set class
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
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