Theorem ecase3d 754

Description: Deduction for elimination by cases.

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	1	com12 11	. 2 |- (ps -> (ph -> th))
3		ecase3d.2	. . 3 |- (ph -> (ch -> th))
4	3	com12 11	. 2 |- (ch -> (ph -> th))
5		ecase3d.3	. . 3 |- (ph -> (-. (ps \/ ch) -> th))
6	5	com12 11	. 2 |- (-. (ps \/ ch) -> (ph -> th))
7	2, 4, 6	ecase3 752	1 |- (ph -> th)

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222

This theorem is referenced by:  distrlem4pr 5130  atcvat4 10324

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

Copyright terms: Public domain