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Theorem nfs1 1731
Description: If  y is not free in  ph,  x is not free in  [ y  /  x ] ph. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfs1.1  |-  F/ y
ph
Assertion
Ref Expression
nfs1  |-  F/ x [ y  /  x ] ph

Proof of Theorem nfs1
StepHypRef Expression
1 nfs1.1 . . . 4  |-  F/ y
ph
21nfri 1453 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3 1730 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1392 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1390   [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-11 1438  ax-4 1441  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687
This theorem is referenced by:  sb8  1778  sb8e  1779
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