ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.77 Unicode version

Theorem pm4.77 789
Description: Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.77  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  <->  ( ( ps  \/  ch )  ->  ph ) )

Proof of Theorem pm4.77
StepHypRef Expression
1 jaob 700 . 2  |-  ( ( ( ps  \/  ch )  ->  ph )  <->  ( ( ps  ->  ph )  /\  ( ch  ->  ph ) ) )
21bicomi 131 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  <->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104    \/ wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator