Theorem dedlemb 839

Description: Lemma for weak deduction theorem. (The proof was shortened by Andrew Salmon, 7-May-2011.)

Assertion

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

Proof of Theorem dedlemb

Step	Hyp	Ref	Expression
1		olc 290	. . 3 |- ((ch /\ -. ph) -> ((ps /\ ph) \/ (ch /\ -. ph)))
2	1	expcom 403	. 2 |- (-. ph -> (ch -> ((ps /\ ph) \/ (ch /\ -. ph))))
3		pm2.21 92	. . . 4 |- (-. ph -> (ph -> ch))
4	3	adantld 426	. . 3 |- (-. ph -> ((ps /\ ph) -> ch))
5		simpl 346	. . . 4 |- ((ch /\ -. ph) -> ch)
6	5	a1i 8	. . 3 |- (-. ph -> ((ch /\ -. ph) -> ch))
7	4, 6	jaod 469	. 2 |- (-. ph -> (((ps /\ ph) \/ (ch /\ -. ph)) -> ch))
8	2, 7	impbid 574	1 |- (-. ph -> (ch <-> ((ps /\ ph) \/ (ch /\ -. ph))))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 163   \/ wo 239   /\ wa 240

This theorem is referenced by:  elimh 841  consensusOLD 845  pm4.42 846  iffalse 2991

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 164  df-or 241  df-an 242

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