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Theorem nf2 1574
Description: An alternative definition of df-nf 1366, 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 1366 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1450 . . . 4  |-  F/ x A. x ph
32nfri 1428 . . 3  |-  ( A. x ph  ->  A. x A. x ph )
4319.23h 1403 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  ( E. x ph  ->  A. x ph ) )
51, 4bitri 177 1  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 102   A.wal 1257   F/wnf 1365   E.wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nf3  1575  nf4dc  1576  nf4r  1577  eusv2i  4215
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