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Theorem nfs1NEW7 29249
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
nfs1.1NEW  |-  F/ y
ph
Assertion
Ref Expression
nfs1NEW7  |-  F/ x [ y  /  x ] ph

Proof of Theorem nfs1NEW7
StepHypRef Expression
1 nfs1.1NEW . . . 4  |-  F/ y
ph
21nfri 1774 . . 3  |-  ( ph  ->  A. y ph )
32hbsb3NEW7 29248 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
43nfi 1557 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1550   [wsb 1655
This theorem is referenced by:  sbco2wAUX7  29288  sb8wAUX7  29294  ax16ALT2OLD7  29427  sbco2OLD7  29436  sb8OLD7  29440
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757  ax-12 1946  ax-7v 29148
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551  df-sb 1656
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