Theorem dedlemb 763

Description: Lemma for weak deduction theorem.

Assertion

Ref	Expression
dedlemb	|- (-. ph -> (ch <-> ((ps /\ ph) \/ (ch /\ -. ph))))

Proof of Theorem dedlemb

Step	Hyp	Ref	Expression
1		olc 268	. . 3 |- ((ch /\ -. ph) -> ((ps /\ ph) \/ (ch /\ -. ph)))
2	1	expcom 374	. 2 |- (-. ph -> (ch -> ((ps /\ ph) \/ (ch /\ -. ph))))
3		pm2.21 76	. . . . 5 |- (-. ph -> (ph -> (ps -> ch)))
4	3	com23 32	. . . 4 |- (-. ph -> (ps -> (ph -> ch)))
5	4	imp3a 361	. . 3 |- (-. ph -> ((ps /\ ph) -> ch))
6		pm3.26 319	. . . 4 |- ((ch /\ -. ph) -> ch)
7	6	a1i 8	. . 3 |- (-. ph -> ((ch /\ -. ph) -> ch))
8	5, 7	jaod 424	. 2 |- (-. ph -> (((ps /\ ph) \/ (ch /\ -. ph)) -> ch))
9	2, 8	impbid 516	1 |- (-. ph -> (ch <-> ((ps /\ ph) \/ (ch /\ -. ph))))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  elimh 764  consensus 767  pm4.42 768  iffalse 2367

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

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