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Theorem nfs1f 1679
Description: If  x is not free in  ph, it is not free in  [ y  /  x ] ph. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfs1f.1  |-  F/ x ph
Assertion
Ref Expression
nfs1f  |-  F/ x [ y  /  x ] ph

Proof of Theorem nfs1f
StepHypRef Expression
1 nfs1f.1 . . . 4  |-  F/ x ph
21nfri 1428 . . 3  |-  ( ph  ->  A. x ph )
32sbh 1675 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
43, 1nfxfr 1379 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1365   [wsb 1661
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-i9 1439  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662
This theorem is referenced by: (None)
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