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

Theorem jao 512
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)
Assertion
Ref Expression
jao  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 511 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
21ex 434 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 368
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 185  df-or 370  df-an 371
This theorem is referenced by:  3jao  1279  suctr  4814  en3lplem2  7833  indpi  9088  jaoded  31287  suctrALT2VD  31584  suctrALT2  31585  en3lplem2VD  31592  hbimpgVD  31652  ax6e2ndeqVD  31657  suctrALTcf  31670  suctrALTcfVD  31671  ax6e2ndeqALT  31679
  Copyright terms: Public domain W3C validator