MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.53 Unicode version

Theorem pm5.53 771
Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.53  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  ->  th )  /\  ( ps  ->  th )
)  /\  ( ch  ->  th ) ) )

Proof of Theorem pm5.53
StepHypRef Expression
1 jaob 758 . 2  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  \/  ps )  ->  th )  /\  ( ch  ->  th ) ) )
2 jaob 758 . . 3  |-  ( ( ( ph  \/  ps )  ->  th )  <->  ( ( ph  ->  th )  /\  ( ps  ->  th ) ) )
32anbi1i 676 . 2  |-  ( ( ( ( ph  \/  ps )  ->  th )  /\  ( ch  ->  th )
)  <->  ( ( (
ph  ->  th )  /\  ( ps  ->  th ) )  /\  ( ch  ->  th )
) )
41, 3bitri 240 1  |-  ( ( ( ( ph  \/  ps )  \/  ch )  ->  th )  <->  ( (
( ph  ->  th )  /\  ( ps  ->  th )
)  /\  ( ch  ->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
  Copyright terms: Public domain W3C validator