Theorem ecase3d 909

Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
ecase3d.1	|- (ph -> (ps -> th))
ecase3d.2	|- (ph -> (ch -> th))
ecase3d.3	|- (ph -> (-. (ps \/ ch) -> th))

Assertion

Ref	Expression
ecase3d	|- (ph -> th)

Proof of Theorem ecase3d

Step	Hyp	Ref	Expression
1		ecase3d.1	. . 3 |- (ph -> (ps -> th))
2		ecase3d.2	. . 3 |- (ph -> (ch -> th))
3	1, 2	jaod 369	. 2 |- (ph -> ((ps \/ ch) -> th))
4		ecase3d.3	. 2 |- (ph -> (-. (ps \/ ch) -> th))
5	3, 4	pm2.61d 150	1 |- (ph -> th)

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357

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

This theorem is referenced by:  ecased  910