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Theorem hbsb3 1731
Description: If  y is not free in  ph,  x is not free in  [ y  /  x ] ph. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbsb3.1  |-  ( ph  ->  A. y ph )
Assertion
Ref Expression
hbsb3  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )

Proof of Theorem hbsb3
StepHypRef Expression
1 hbsb3.1 . . 3  |-  ( ph  ->  A. y ph )
21sbimi 1689 . 2  |-  ( [ y  /  x ] ph  ->  [ y  /  x ] A. y ph )
3 hbsb2a 1729 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )
42, 3syl 14 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   [wsb 1687
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-11 1438  ax-4 1441  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by:  nfs1  1732  sbcof2  1733  ax16  1736  sb8h  1777  sb8eh  1778  ax16ALT  1782
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