Theorem jaoa 496

Description: Inference disjoining and conjoining the antecedents of two implications. (Contributed by Stefan Allan, 1-Nov-2008.)

Hypotheses

Ref	Expression
jaao.1	|- (ph -> (ps -> ch))
jaao.2	|- (th -> (ta -> ch))

Assertion

Ref	Expression
jaoa	|- ((ph \/ th) -> ((ps /\ ta) -> ch))

Proof of Theorem jaoa

Step	Hyp	Ref	Expression
1		jaao.1	. . 3 |- (ph -> (ps -> ch))
2	1	adantrd 454	. 2 |- (ph -> ((ps /\ ta) -> ch))
3		jaao.2	. . 3 |- (th -> (ta -> ch))
4	3	adantld 453	. 2 |- (th -> ((ps /\ ta) -> ch))
5	2, 4	jaoi 368	1 |- ((ph \/ th) -> ((ps /\ ta) -> ch))

Syntax hints:   -> wi 4   \/ wo 357   /\ wa 358

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 177  df-or 359  df-an 360

This theorem is referenced by:  pm4.79  566