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Theorem nf3 1893
Description: An alternative definition of df-nf 1555. (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 1892 . 2  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
2 nfe1 1750 . . 3  |-  F/ x E. x ph
3219.21 1817 . 2  |-  ( A. x ( E. x ph  ->  ph )  <->  ( E. x ph  ->  A. x ph ) )
41, 3bitr4i 245 1  |-  ( F/ x ph  <->  A. x
( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   A.wal 1550   E.wex 1551   F/wnf 1554
This theorem is referenced by:  eusv2nf  4756  xfree  23985
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-11 1764
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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