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Theorem spsbim 2243
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 2202 . 2  |-  ( A. x ( ph  ->  ps )  ->  [ y  /  x ] ( ph  ->  ps ) )
2 sbi1 2241 . 2  |-  ( [ y  /  x ]
( ph  ->  ps )  ->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps ) )
31, 2syl 17 1  |-  ( A. x ( ph  ->  ps )  ->  ( [
y  /  x ] ph  ->  [ y  /  x ] ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450   [wsb 1805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806
This theorem is referenced by:  mo3  2356  bj-hbsb3t  31379  wl-mo3t  31975  pm11.59  36811  sbiota1  36855
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