Theorem jao 534

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

Step	Hyp	Ref	Expression
1		pm3.44 533	. 2 |- ( ( ( ph -> ps ) /\ ( ch -> ps ) ) -> ( ( ph \/ ch ) -> ps ) )
2	1	ex 450	1 |- ( ( ph -> ps ) -> ( ( ch -> ps ) -> ( ( ph \/ ch ) -> ps ) ) )

Syntax hints:   -> wi 4   \/ wo 383

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 197  df-or 385  df-an 386

This theorem is referenced by:  3jao  1389  suctrOLD  5809  en3lplem2  8512  indpi  9729  bj-orim2  32541  bj-currypeirce  32544  jaoded  38782  suctrALT2VD  39071  suctrALT2  39072  en3lplem2VD  39079  hbimpgVD  39140  ax6e2ndeqVD  39145  suctrALTcf  39158  suctrALTcfVD  39159  ax6e2ndeqALT  39167