Theorem ecase3d 560

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 13	. 2 |- (ps -> (ph -> th))
3		ecase3d.2	. . 3 |- (ph -> (ch -> th))
4	3	com12 13	. 2 |- (ch -> (ph -> th))
5		ecase3d.3	. . 3 |- (ph -> (-. (ps \/ ch) -> th))
6	5	com12 13	. 2 |- (-. (ps \/ ch) -> (ph -> th))
7	2, 4, 6	ecase3 559	1 |- (ph -> th)

Syntax hints:  -. wn 1   -> wi 2   \/ wo 195

This theorem is referenced by:  distrlem4pr 3924  atcvat4 5775

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

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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