Theorem jaoded 38782

Description: Deduction form of jao 534. Disjunction of antecedents. (Contributed by Alan Sare, 3-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
jaoded.1	|- ( ph -> ( ps -> ch ) )
jaoded.2	|- ( th -> ( ta -> ch ) )
jaoded.3	|- ( et -> ( ps \/ ta ) )

Assertion

Ref	Expression
jaoded	|- ( ( ph /\ th /\ et ) -> ch )

Proof of Theorem jaoded

Step	Hyp	Ref	Expression
1		jaoded.1	. 2 |- ( ph -> ( ps -> ch ) )
2		jaoded.2	. 2 |- ( th -> ( ta -> ch ) )
3		jaoded.3	. 2 |- ( et -> ( ps \/ ta ) )
4		jao 534	. . 3 |- ( ( ps -> ch ) -> ( ( ta -> ch ) -> ( ( ps \/ ta ) -> ch ) ) )
5	4	3imp 1256	. 2 |- ( ( ( ps -> ch ) /\ ( ta -> ch ) /\ ( ps \/ ta ) ) -> ch )
6	1, 2, 3, 5	syl3an 1368	1 |- ( ( ph /\ th /\ et ) -> ch )

Syntax hints:   -> wi 4   \/ wo 383   /\ w3a 1037

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  df-3an 1039

This theorem is referenced by:  suctrALT3  39160