Theorem ecased 910

Description: Deduction for elimination by cases. (Contributed by NM, 8-Oct-2012.)

Hypotheses

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

Assertion

Ref	Expression
ecased	|- (ph -> th)

Proof of Theorem ecased

Step	Hyp	Ref	Expression
1		ecased.1	. 2 |- (ph -> (-. ps -> th))
2		ecased.2	. 2 |- (ph -> (-. ch -> th))
3		pm3.11 485	. . 3 |- (-. (-. ps \/ -. ch) -> (ps /\ ch))
4		ecased.3	. . 3 |- (ph -> ((ps /\ ch) -> th))
5	3, 4	syl5 28	. 2 |- (ph -> (-. (-. ps \/ -. ch) -> th))
6	1, 2, 5	ecase3d 909	1 |- (ph -> th)

Syntax hints:  -. wn 3   -> 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:  ecase3ad  911