Theorem exp3acom23g 1371

Description: Implication form of exp3acom23 1372. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Assertion

Ref	Expression
exp3acom23g	|- ((ph -> ((ps /\ ch) -> th)) <-> (ph -> (ch -> (ps -> th))))

Proof of Theorem exp3acom23g

Step	Hyp	Ref	Expression
1		ancomsimp 1369	. . 3 |- (((ps /\ ch) -> th) <-> ((ch /\ ps) -> th))
2		impexp 433	. . 3 |- (((ch /\ ps) -> th) <-> (ch -> (ps -> th)))
3	1, 2	bitri 240	. 2 |- (((ps /\ ch) -> th) <-> (ch -> (ps -> th)))
4	3	imbi2i 303	1 |- ((ph -> ((ps /\ ch) -> th)) <-> (ph -> (ch -> (ps -> th))))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by: (None)