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Theorem nfsb2 2011
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 nfnae 1909 . 2  |-  F/ x  -.  A. x  x  =  y
2 hbsb2 2010 . 2  |-  ( -. 
A. x  x  =  y  ->  ( [
y  /  x ] ph  ->  A. x [ y  /  x ] ph ) )
31, 2nfd 1758 1  |-  ( -. 
A. x  x  =  y  ->  F/ x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   F/wnf 1534   [wsb 1638
This theorem is referenced by:  sbequi  2012  nfsb4t  2033  sbco3  2041
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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