Theorem pm2.81 579

Description: Theorem *2.81 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.81	|- ((ps -> (ch -> th)) -> ((ph \/ ps) -> ((ph \/ ch) -> (ph \/ th))))

Proof of Theorem pm2.81

Step	Hyp	Ref	Expression
1		orim2 570	. 2 |- ((ps -> (ch -> th)) -> ((ph \/ ps) -> (ph \/ (ch -> th))))
2		pm2.76 577	. 2 |- ((ph \/ (ch -> th)) -> ((ph \/ ch) -> (ph \/ th)))
3	1, 2	syl6 22	1 |- ((ps -> (ch -> th)) -> ((ph \/ ps) -> ((ph \/ ch) -> (ph \/ th))))

Syntax hints:   -> 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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