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Theorem nfsb2 2102
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 1908 . 2  |-  F/ x  -.  A. x  x  =  y
2 hbsb2 2101 . 2  |-  ( -. 
A. x  x  =  y  ->  ( [
y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
31, 2nfd 1883 1  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1396   F/wnf 1621   [wsb 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622  df-sb 1745
This theorem is referenced by:  nfsb4t  2132  sbco3  2162  sb9  2171  wl-nfs1t  30231
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