Theorem pm5.33 652

Description: Theorem *5.33 of [WhiteheadRussell] p. 125.

Assertion

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

Proof of Theorem pm5.33

Step	Hyp	Ref	Expression
1		ibar 645	. . 3 |- (ph -> (ps <-> (ph /\ ps)))
2	1	imbi1d 615	. 2 |- (ph -> ((ps -> ch) <-> ((ph /\ ps) -> ch)))
3	2	pm5.32i 647	1 |- ((ph /\ (ps -> ch)) <-> (ph /\ ((ph /\ ps) -> 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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