Theorem pm5.42 318

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 299	. . 3 |- ( ph -> ( ch <-> ( ph /\ ch ) ) )
2	1	imbi2d 229	. 2 |- ( ph -> ( ( ps -> ch ) <-> ( ps -> ( ph /\ ch ) ) ) )
3	2	pm5.74i 179	1 |- ( ( ph -> ( ps -> ch ) ) <-> ( ph -> ( ps -> ( ph /\ ch ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  anc2l  325  imdistan  441