Theorem ecased 643

Description: Deduction for elimination by cases.

Hypotheses

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

Assertion

Ref	Expression
ecased	|- (ph -> ps)

Proof of Theorem ecased

Step	Hyp	Ref	Expression
1		ecased.2	. . . 4 |- (ph -> -. ch)
2		ecased.3	. . . 4 |- (ph -> -. th)
3	1, 2	jca 236	. . 3 |- (ph -> (-. ch /\ -. th))
4		ioran 254	. . 3 |- (-. (ch \/ th) <-> (-. ch /\ -. th))
5	3, 4	sylibr 175	. 2 |- (ph -> -. (ch \/ th))
6		ecased.1	. . . 4 |- (ph -> (ps \/ ch \/ th))
7		3orass 584	. . . 4 |- ((ps \/ ch \/ th) <-> (ps \/ (ch \/ th)))
8	6, 7	sylib 173	. . 3 |- (ph -> (ps \/ (ch \/ th)))
9	8	ord 202	. 2 |- (ph -> (-. ps -> (ch \/ th)))
10	5, 9	mt3d 101	1 |- (ph -> ps)

Syntax hints:  -. wn 1   -> wi 2   \/ wo 195   /\ wa 196   \/ w3o 580

This theorem is referenced by:  tz7.7 2224

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  df-3or 582

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