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Theorem nfsb2 2200
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 1995 . 2  |-  F/ x  -.  A. x  x  =  y
2 hbsb2 2199 . 2  |-  ( -. 
A. x  x  =  y  ->  ( [
y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
31, 2nfd 1966 1  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1452   F/wnf 1677   [wsb 1807
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943  ax-13 2101
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-nf 1678  df-sb 1808
This theorem is referenced by:  nfsb4t  2228  sbco3  2256  sb9  2265  wl-nfs1t  31915
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