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Theorem nfs1 1997
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 1754 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3 1996 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1541 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1534   [wsb 1638
This theorem is referenced by:  ax16ALT2  2001  sbco2  2039  sb8  2045  mo  2178  mo5f  23159
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-ex 1532  df-nf 1535  df-sb 1639
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