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Theorem sbimv 1815
Description: Intuitionistic proof of sbim 1869 where  x and  y are distinct. (Contributed by Jim Kingdon, 18-Jan-2018.)
Assertion
Ref Expression
sbimv  |-  ( [ y  /  x ]
( ph  ->  ps )  <->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps )
)
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    ps( x, y)

Proof of Theorem sbimv
StepHypRef Expression
1 sbi1v 1813 . 2  |-  ( [ y  /  x ]
( ph  ->  ps )  ->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps ) )
2 sbi2v 1814 . 2  |-  ( ( [ y  /  x ] ph  ->  [ y  /  x ] ps )  ->  [ y  /  x ] ( ph  ->  ps ) )
31, 2impbii 124 1  |-  ( [ y  /  x ]
( ph  ->  ps )  <->  ( [ y  /  x ] ph  ->  [ y  /  x ] ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   [wsb 1686
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-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-sb 1687
This theorem is referenced by:  sblimv  1816  sbim  1869
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