Theorem dedlem0b 568

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 71	. . . 4 |- (-. ph -> (ph -> (ch /\ ph)))
2	1	syl3d 26	. . 3 |- (-. ph -> ((ps -> ph) -> (ps -> (ch /\ ph))))
3	2	com23 32	. 2 |- (-. ph -> (ps -> ((ps -> ph) -> (ch /\ ph))))
4		pm2.21 71	. . . . 5 |- (-. ps -> (ps -> ph))
5		pm3.27 260	. . . . 5 |- ((ch /\ ph) -> ph)
6	4, 5	syl34 20	. . . 4 |- (((ps -> ph) -> (ch /\ ph)) -> (-. ps -> ph))
7	6	con1d 85	. . 3 |- (((ps -> ph) -> (ch /\ ph)) -> (-. ph -> ps))
8	7	com12 13	. 2 |- (-. ph -> (((ps -> ph) -> (ch /\ ph)) -> ps))
9	3, 8	impbid 397	1 |- (-. ph -> (ps <-> ((ps -> ph) -> (ch /\ ph))))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   /\ wa 196

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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