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Theorem spsbim 2016
Description: Specialization of implication. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
spsbim  |-  ( A. x ( ph  ->  ps )  ->  ( [
y  /  x ] ph  ->  [ y  /  x ] ps ) )

Proof of Theorem spsbim
StepHypRef Expression
1 stdpc4 1964 . 2  |-  ( A. x ( ph  ->  ps )  ->  [ y  /  x ] ( ph  ->  ps ) )
2 sbi1 2003 . 2  |-  ( [ y  /  x ]
( ph  ->  ps )  ->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps ) )
31, 2syl 15 1  |-  ( A. x ( ph  ->  ps )  ->  ( [
y  /  x ] ph  ->  [ y  /  x ] ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   [wsb 1629
This theorem is referenced by:  pm11.59  27590  sbiota1  27634
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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