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

Step	Hyp	Ref	Expression
1		pm3.44 511	. 2 |- ( ( ( ph -> ps ) /\ ( ch -> ps ) ) -> ( ( ph \/ ch ) -> ps ) )
2	1	ex 434	1 |- ( ( ph -> ps ) -> ( ( ch -> ps ) -> ( ( ph \/ ch ) -> ps ) ) )

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