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Theorem hbs1f 1737
Description: If  x is not free in  ph, it is not free in  [ y  /  x ] ph. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
hbs1f.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbs1f  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )

Proof of Theorem hbs1f
StepHypRef Expression
1 hbs1f.1 . . 3  |-  ( ph  ->  A. x ph )
21sbh 1732 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
32, 1hbxfrbi 1431 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312   [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-i9 1493  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-sb 1719
This theorem is referenced by: (None)
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