Theorem ecase23d 920

Description: Deduction for elimination by cases.

Hypotheses

Ref	Expression
ecase23d.1	|- (ph -> -. ch)
ecase23d.2	|- (ph -> -. th)
ecase23d.3	|- (ph -> (ps \/ ch \/ th))

Assertion

Ref	Expression
ecase23d	|- (ph -> ps)

Proof of Theorem ecase23d

Step	Hyp	Ref	Expression
1		ecase23d.1	. . . 4 |- (ph -> -. ch)
2		ecase23d.2	. . . 4 |- (ph -> -. th)
3	1, 2	jca 288	. . 3 |- (ph -> (-. ch /\ -. th))
4		ioran 306	. . 3 |- (-. (ch \/ th) <-> (-. ch /\ -. th))
5	3, 4	sylibr 200	. 2 |- (ph -> -. (ch \/ th))
6		ecase23d.3	. . . 4 |- (ph -> (ps \/ ch \/ th))
7		3orass 777	. . . 4 |- ((ps \/ ch \/ th) <-> (ps \/ (ch \/ th)))
8	6, 7	sylib 198	. . 3 |- (ph -> (ps \/ (ch \/ th)))
9	8	ord 232	. 2 |- (ph -> (-. ps -> (ch \/ th)))
10	5, 9	mt3d 114	1 |- (ph -> ps)

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222   /\ wa 223   \/ w3o 773

This theorem is referenced by:  tz7.7 2968

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  df-3or 775

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