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Theorem nfs1 2104
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 1780 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3 2103 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1561 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1554   [wsb 1659
This theorem is referenced by:  ax16ALT2  2161  sbco2  2167  sb8  2174  sb8e  2175
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 1668  ax-8 1689  ax-6 1746  ax-11 1763  ax-12 1953
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660
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