MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.48 Structured version   Unicode version

Theorem pm3.48 841
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.)
Assertion
Ref Expression
pm3.48  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 386 . . 3  |-  ( ps 
->  ( ps  \/  th ) )
21imim2i 16 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  th ) ) )
3 olc 385 . . 3  |-  ( th 
->  ( ps  \/  th ) )
43imim2i 16 . 2  |-  ( ( ch  ->  th )  ->  ( ch  ->  ( ps  \/  th ) ) )
52, 4jaao 511 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 369    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372
This theorem is referenced by:  orim12d  846  tz7.48lem  7113  caubnd  13365
  Copyright terms: Public domain W3C validator