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Theorem nfs1 2194
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 1956 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3 2193 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1677 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1670   [wsb 1800
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1672  ax-4 1685  ax-5 1761  ax-6 1808  ax-7 1854  ax-10 1918  ax-12 1936  ax-13 2091
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1667  df-nf 1671  df-sb 1801
This theorem is referenced by:  sb8  2253  sb8e  2254
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