Theorem pm5.3 446

Description: Theorem *5.3 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.3	|- (((ph /\ ps) -> ch) <-> ((ph /\ ps) -> (ph /\ ch)))

Proof of Theorem pm5.3

Step	Hyp	Ref	Expression
1		pm3.3 348	. . 3 |- (((ph /\ ps) -> ch) -> (ph -> (ps -> ch)))
2	1	imdistand 445	. 2 |- (((ph /\ ps) -> ch) -> ((ph /\ ps) -> (ph /\ ch)))
3		pm3.27 323	. . 3 |- ((ph /\ ch) -> ch)
4	3	imim2i 17	. 2 |- (((ph /\ ps) -> (ph /\ ch)) -> ((ph /\ ps) -> ch))
5	2, 4	impbi 157	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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