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Theorem nf2 1885
Description: An alternative definition of df-nf 1551, 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 1551 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1802 . . 3  |-  F/ x A. x ph
3219.23 1815 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  ( E. x ph  ->  A. x ph ) )
41, 3bitri 241 1  |-  ( F/ x ph  <->  ( E. x ph  ->  A. x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546   E.wex 1547   F/wnf 1550
This theorem is referenced by:  nf3  1886  nf4  1887  ax12olem3  1974  equveli  2042  eusv2i  4679
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551
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