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Theorem nf2 1876
Description: An alternative definition of df-nf 1550, 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 1550 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1794 . . 3  |-  F/ x A. x ph
3219.23 1807 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  ( E. x ph  ->  A. x ph ) )
41, 3bitri 240 1  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1545   E.wex 1546   F/wnf 1549
This theorem is referenced by:  nf3  1877  nf4  1878  eusv2i  4634
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-11 1751
This theorem depends on definitions:  df-bi 177  df-ex 1547  df-nf 1550
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