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Theorem nf3 1630
Description: An alternate definition of df-nf 1420. (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 1629 . 2  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
2 nfe1 1455 . . . 4  |-  F/ x E. x ph
32nfri 1482 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
4319.21h 1519 . 2  |-  ( A. x ( E. x ph  ->  ph )  <->  ( E. x ph  ->  A. x ph ) )
51, 4bitr4i 186 1  |-  ( F/ x ph  <->  A. x
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   F/wnf 1419   E.wex 1451
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  eusv2nf  4337
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