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Theorem nfs1 1984
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 1742 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3 1983 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1538 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1531   [wsb 1629
This theorem is referenced by:  ax16ALT2  1988  sbco2  2026  sb8  2032  mo  2165  mo5f  23143
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
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