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Theorem nfs1f 2178
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 2175 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
32, 1nfxfr 1693 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1664   [wsb 1787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906  ax-13 2054
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661  df-nf 1665  df-sb 1788
This theorem is referenced by: (None)
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