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Theorem nf2 1778
Description: An alternative definition of df-nf 1540, 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 1540 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1719 . . 3  |-  F/ x A. x ph
3219.23 1777 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  ( E. x ph  ->  A. x ph ) )
41, 3bitri 242 1  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E.wex 1537   F/wnf 1539
This theorem is referenced by:  nf3  1779  nf4  1780  eusv2i  4503
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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