Theorem jaoian 759

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)

Hypotheses

Ref	Expression
jaoian.1	|- ((ph /\ ps) -> ch)
jaoian.2	|- ((th /\ ps) -> ch)

Assertion

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

Proof of Theorem jaoian

Step	Hyp	Ref	Expression
1		jaoian.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 423	. . 3 |- (ph -> (ps -> ch))
3		jaoian.2	. . . 4 |- ((th /\ ps) -> ch)
4	3	ex 423	. . 3 |- (th -> (ps -> ch))
5	2, 4	jaoi 368	. 2 |- ((ph \/ th) -> (ps -> ch))
6	5	imp 418	1 |- (((ph \/ th) /\ ps) -> 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:  ccase  912