Theorem dedlem0a 758

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

Assertion

Ref	Expression
dedlem0a	|- (ph -> (ps <-> ((ch -> ph) -> (ps /\ ph))))

Proof of Theorem dedlem0a

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- (ps -> ((ch -> ph) -> ps))
2		ax-1 4	. . . . 5 |- (ph -> (ch -> ph))
3	2	imim1i 16	. . . 4 |- (((ch -> ph) -> ps) -> (ph -> ps))
4	3	com12 11	. . 3 |- (ph -> (((ch -> ph) -> ps) -> ps))
5	1, 4	impbid2 516	. 2 |- (ph -> (ps <-> ((ch -> ph) -> ps)))
6		iba 640	. . 3 |- (ph -> (ps <-> (ps /\ ph)))
7	6	imbi2d 610	. 2 |- (ph -> (((ch -> ph) -> ps) <-> ((ch -> ph) -> (ps /\ ph))))
8	5, 7	bitrd 526	1 |- (ph -> (ps <-> ((ch -> ph) -> (ps /\ ph))))

Syntax hints:   -> 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