Theorem dedlemb 970

Description: Lemma for iffalse 3544. (Contributed by NM, 15-May-1999.) (Proof 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 711	. . 3 |- ( ( ch /\ -. ph ) -> ( ( ps /\ ph ) \/ ( ch /\ -. ph ) ) )
2	1	expcom 116	. 2 |- ( -. ph -> ( ch -> ( ( ps /\ ph ) \/ ( ch /\ -. ph ) ) ) )
3		pm2.21 617	. . . 4 |- ( -. ph -> ( ph -> ch ) )
4	3	adantld 278	. . 3 |- ( -. ph -> ( ( ps /\ ph ) -> ch ) )
5		simpl 109	. . . 4 |- ( ( ch /\ -. ph ) -> ch )
6	5	a1i 9	. . 3 |- ( -. ph -> ( ( ch /\ -. ph ) -> ch ) )
7	4, 6	jaod 717	. 2 |- ( -. ph -> ( ( ( ps /\ ph ) \/ ( ch /\ -. ph ) ) -> ch ) )
8	2, 7	impbid 129	1 |- ( -. ph -> ( ch <-> ( ( ps /\ ph ) \/ ( ch /\ -. ph ) ) ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   <-> wb 105   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  iffalse  3544