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Theorem nf2 1601
Description: An alternate definition of df-nf 1393, which does not involve nested quantifiers on the same variable. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf2  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )

Proof of Theorem nf2
StepHypRef Expression
1 df-nf 1393 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1477 . . . 4  |-  F/ x A. x ph
32nfri 1455 . . 3  |-  ( A. x ph  ->  A. x A. x ph )
4319.23h 1430 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  ( E. x ph  ->  A. x ph ) )
51, 4bitri 182 1  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1285   F/wnf 1392   E.wex 1424
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-gen 1381  ax-ie2 1426  ax-4 1443  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  nf3  1602  nf4dc  1603  nf4r  1604  eusv2i  4253
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