Theorem dedlembOLD 840

Description: Lemma for weak deduction theorem.

Assertion

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

Proof of Theorem dedlembOLD

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	. . . . 5 |- (-. ph -> (ph -> (ps -> ch)))
4	3	com23 36	. . . 4 |- (-. ph -> (ps -> (ph -> ch)))
5	4	imp3a 388	. . 3 |- (-. ph -> ((ps /\ ph) -> ch))
6		simpl 346	. . . 4 |- ((ch /\ -. ph) -> ch)
7	6	a1i 8	. . 3 |- (-. ph -> ((ch /\ -. ph) -> ch))
8	5, 7	jaod 469	. 2 |- (-. ph -> (((ps /\ ph) \/ (ch /\ -. ph)) -> ch))
9	2, 8	impbid 574	1 |- (-. ph -> (ch <-> ((ps /\ ph) \/ (ch /\ -. ph))))

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

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

Copyright terms: Public domain