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Theorem nfs1f 2122
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 . . 3  |-  F/ x ph
21sbf 2119 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
32, 1nfxfr 1580 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1554   [wsb 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660
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