Theorem pm5.33 848

Description: Theorem *5.33 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.33	|- ((ph /\ (ps -> ch)) <-> (ph /\ ((ph /\ ps) -> ch)))

Proof of Theorem pm5.33

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 |- (ph -> (ps <-> (ph /\ ps)))
2	1	imbi1d 308	. 2 |- (ph -> ((ps -> ch) <-> ((ph /\ ps) -> ch)))
3	2	pm5.32i 618	1 |- ((ph /\ (ps -> ch)) <-> (ph /\ ((ph /\ ps) -> ch)))

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)