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Theorem hbs1f 1711
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 1706 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
32, 1hbxfrbi 1406 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287   [wsb 1692
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-i9 1468  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-sb 1693
This theorem is referenced by: (None)
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