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Theorem hbsb3 2095
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 1664 . 2  |-  ( [ y  /  x ] ph  ->  [ y  /  x ] A. y ph )
3 hbsb2a 2093 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )
42, 3syl 16 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   [wsb 1658
This theorem is referenced by:  nfs1  2096  ax16ALT  2131
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659
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