Theorem dedlem0b 761

Description: Lemma for an alternate version of weak deduction theorem.

Assertion

Ref	Expression
dedlem0b	|- (-. ph -> (ps <-> ((ps -> ph) -> (ch /\ ph))))

Proof of Theorem dedlem0b

Step	Hyp	Ref	Expression
1		pm2.21 76	. . . 4 |- (-. ph -> (ph -> (ch /\ ph)))
2	1	imim2d 25	. . 3 |- (-. ph -> ((ps -> ph) -> (ps -> (ch /\ ph))))
3	2	com23 32	. 2 |- (-. ph -> (ps -> ((ps -> ph) -> (ch /\ ph))))
4		pm2.21 76	. . . . 5 |- (-. ps -> (ps -> ph))
5		pm3.27 323	. . . . 5 |- ((ch /\ ph) -> ph)
6	4, 5	imim12i 18	. . . 4 |- (((ps -> ph) -> (ch /\ ph)) -> (-. ps -> ph))
7	6	con1d 93	. . 3 |- (((ps -> ph) -> (ch /\ ph)) -> (-. ph -> ps))
8	7	com12 11	. 2 |- (-. ph -> (((ps -> ph) -> (ch /\ ph)) -> ps))
9	3, 8	impbid 516	1 |- (-. ph -> (ps <-> ((ps -> ph) -> (ch /\ ph))))

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

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-an 225

Copyright terms: Public domain