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Theorem nf3 1669
Description: An alternate definition of df-nf 1461. (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 1668 . 2  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
2 nfe1 1496 . . . 4  |-  F/ x E. x ph
32nfri 1519 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
4319.21h 1557 . 2  |-  ( A. x ( E. x ph  ->  ph )  <->  ( E. x ph  ->  A. x ph ) )
51, 4bitr4i 187 1  |-  ( F/ x ph  <->  A. x
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   A.wal 1351   F/wnf 1460   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461
This theorem is referenced by:  hbe1a  2023  eusv2nf  4453
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