Theorem pm2.74 575

Description: Theorem *2.74 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.74	|- ((ps -> ph) -> (((ph \/ ps) \/ ch) -> (ph \/ ch)))

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		orel2 252	. . 3 |- (-. ps -> ((ph \/ ps) -> ph))
2	1	orim1d 568	. 2 |- (-. ps -> (((ph \/ ps) \/ ch) -> (ph \/ ch)))
3		orc 269	. . 3 |- (ph -> (ph \/ ch))
4	3	a1d 12	. 2 |- (ph -> (((ph \/ ps) \/ ch) -> (ph \/ ch)))
5	2, 4	ja 137	1 |- ((ps -> ph) -> (((ph \/ ps) \/ ch) -> (ph \/ ch)))

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222

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-or 224  df-an 225

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