Theorem pm2.75 572

Description: Theorem *2.75 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.75	|- ((ph \/ ps) -> ((ph \/ (ps -> ch)) -> (ph \/ ch)))

Proof of Theorem pm2.75

Step	Hyp	Ref	Expression
1		orc 269	. . 3 |- (ph -> (ph \/ ch))
2	1	a1d 12	. 2 |- (ph -> ((ph \/ (ps -> ch)) -> (ph \/ ch)))
3		pm2.27 62	. . 3 |- (ps -> ((ps -> ch) -> ch))
4	3	orim2d 565	. 2 |- (ps -> ((ph \/ (ps -> ch)) -> (ph \/ ch)))
5	2, 4	jaoi 341	1 |- ((ph \/ ps) -> ((ph \/ (ps -> ch)) -> (ph \/ ch)))

Syntax hints:   -> wi 3   \/ wo 222

This theorem is referenced by:  pm2.76 573

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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