Theorem jao 515

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		pm3.44 514	. 2 |- ( ( ( ph -> ps ) /\ ( ch -> ps ) ) -> ( ( ph \/ ch ) -> ps ) )
2	1	ex 436	1 |- ( ( ph -> ps ) -> ( ( ch -> ps ) -> ( ( ph \/ ch ) -> ps ) ) )

Syntax hints:   -> wi 4   \/ wo 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 189  df-or 372  df-an 373

This theorem is referenced by:  3jao  1328  suctr  5505  en3lplem2  8117  indpi  9329  jaoded  36927  suctrALT2VD  37226  suctrALT2  37227  en3lplem2VD  37234  hbimpgVD  37295  ax6e2ndeqVD  37300  suctrALTcf  37313  suctrALTcfVD  37314  ax6e2ndeqALT  37322