Theorem pm5.42 531

Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.42	|- ((ph -> (ps -> ch)) <-> (ph -> (ps -> (ph /\ ch))))

Proof of Theorem pm5.42

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 |- (ph -> (ch <-> (ph /\ ch)))
2	1	imbi2d 307	. 2 |- (ph -> ((ps -> ch) <-> (ps -> (ph /\ ch))))
3	2	pm5.74i 236	1 |- ((ph -> (ps -> ch)) <-> (ph -> (ps -> (ph /\ 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:  anc2l  538  imdistan  670