Theorem dedlema 1110

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

Assertion

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

Proof of Theorem dedlema

Step	Hyp	Ref	Expression
1		orc 472	. . 3 |- ((ps /\ ph) -> ((ps /\ ph) \/ (ch /\ -. ph)))
2	1	expcom 495	. 2 |- (ph -> (ps -> ((ps /\ ph) \/ (ch /\ -. ph))))
3		simpl 533	. . . 4 |- ((ps /\ ph) -> ps)
4	3	a1i 8	. . 3 |- (ph -> ((ps /\ ph) -> ps))
5		pm2.24 131	. . . 4 |- (ph -> (-. ph -> ps))
6	5	adantld 546	. . 3 |- (ph -> ((ch /\ -. ph) -> ps))
7	4, 6	jaod 550	. 2 |- (ph -> (((ps /\ ph) \/ (ch /\ -. ph)) -> ps))
8	2, 7	impbid 250	1 |- (ph -> (ps <-> ((ps /\ ph) \/ (ch /\ -. ph))))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 231   \/ wo 432   /\ wa 433

This theorem is referenced by:  elimh 1112  dedt 1113  pm4.42 1117

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 232  df-or 434  df-an 435

Copyright terms: Public domain