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Theorem nf3 1600
Description: An alternate definition of df-nf 1391. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf3  |-  ( F/ x ph  <->  A. x
( E. x ph  ->  ph ) )

Proof of Theorem nf3
StepHypRef Expression
1 nf2 1599 . 2  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
2 nfe1 1426 . . . 4  |-  F/ x E. x ph
32nfri 1453 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
4319.21h 1490 . 2  |-  ( A. x ( E. x ph  ->  ph )  <->  ( E. x ph  ->  A. x ph ) )
51, 4bitr4i 185 1  |-  ( F/ x ph  <->  A. x
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   F/wnf 1390   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  eusv2nf  4214
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