Theorem jaodan 760

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 14-Oct-2005.)

Hypotheses

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

Assertion

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

Proof of Theorem jaodan

Step	Hyp	Ref	Expression
1		jaodan.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 423	. . 3 |- (ph -> (ps -> ch))
3		jaodan.2	. . . 4 |- ((ph /\ th) -> ch)
4	3	ex 423	. . 3 |- (ph -> (th -> ch))
5	2, 4	jaod 369	. 2 |- (ph -> ((ps \/ th) -> ch))
6	5	imp 418	1 |- ((ph /\ (ps \/ th)) -> 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:  mpjaodan  761  andi  837  ccase  912