Theorem pm5.42 652

Description: Theorem *5.42 of [WhiteheadRussell] p. 125.

Assertion

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

Proof of Theorem pm5.42

Step	Hyp	Ref	Expression
1		ibar 643	. . 3 |- (ph -> (ch <-> (ph /\ ch)))
2	1	imbi2d 612	. 2 |- (ph -> ((ps -> ch) <-> (ps -> (ph /\ ch))))
3	2	pm5.74i 584	1 |- ((ph -> (ps -> ch)) <-> (ph -> (ps -> (ph /\ ch))))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

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 147  df-an 225

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