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Theorem bj-nfs1t 31255
Description: A theorem close to a closed form of nfs1 2155. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfs1t  |-  ( A. x ( ph  ->  A. y ph )  ->  F/ x [ y  /  x ] ph )

Proof of Theorem bj-nfs1t
StepHypRef Expression
1 bj-hbsb3t 31253 . . 3  |-  ( A. x ( ph  ->  A. y ph )  -> 
( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
21axc4i 1952 . 2  |-  ( A. x ( ph  ->  A. y ph )  ->  A. x ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
3 df-nf 1664 . 2  |-  ( F/ x [ y  /  x ] ph  <->  A. x
( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
42, 3sylibr 215 1  |-  ( A. x ( ph  ->  A. y ph )  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1663   [wsb 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-12 1904  ax-13 2052
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1787
This theorem is referenced by:  bj-nfs1t2  31256
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