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Theorem nfsb2 2057
Description: Bound-variable hypothesis builder for substitution. (Contributed by Mario Carneiro, 4-Oct-2016.)
Assertion
Ref Expression
nfsb2  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )

Proof of Theorem nfsb2
StepHypRef Expression
1 nfna1 1839 . 2  |-  F/ x  -.  A. x  x  =  y
2 hbsb2 2056 . 2  |-  ( -. 
A. x  x  =  y  ->  ( [
y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
31, 2nfd 1814 1  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1368   F/wnf 1590   [wsb 1702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794  ax-13 1952
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703
This theorem is referenced by:  nfsb4t  2087  sbco3  2121  sbco3OLD  2122  sb9  2133  wl-nfs1t  28507
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