Theorem dedlem0a 834

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

Assertion

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

Proof of Theorem dedlem0a

Step	Hyp	Ref	Expression
1		pm3.21 306	. . 3 |- (ph -> (ps -> (ps /\ ph)))
2	1	a1dd 53	. 2 |- (ph -> (ps -> ((ch -> ph) -> (ps /\ ph))))
3		ax-1 4	. . . 4 |- (ph -> (ch -> ph))
4		simpl 346	. . . 4 |- ((ps /\ ph) -> ps)
5	3, 4	imim12i 21	. . 3 |- (((ch -> ph) -> (ps /\ ph)) -> (ph -> ps))
6	5	com12 14	. 2 |- (ph -> (((ch -> ph) -> (ps /\ ph)) -> ps))
7	2, 6	impbid 574	1 |- (ph -> (ps <-> ((ch -> ph) -> (ps /\ ph))))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  iftrue 2989

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 164  df-an 242

Copyright terms: Public domain