Theorem pm2.82 576

Description: Theorem *2.82 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
pm2.82	|- (((ph \/ ps) \/ ch) -> (((ph \/ -. ch) \/ th) -> ((ph \/ ps) \/ th)))

Proof of Theorem pm2.82

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- ((ph \/ ps) -> ((ph \/ -. ch) -> (ph \/ ps)))
2		pm2.24 79	. . . 4 |- (ch -> (-. ch -> ps))
3	2	orim2d 565	. . 3 |- (ch -> ((ph \/ -. ch) -> (ph \/ ps)))
4	1, 3	jaoi 341	. 2 |- (((ph \/ ps) \/ ch) -> ((ph \/ -. ch) -> (ph \/ ps)))
5	4	orim1d 564	1 |- (((ph \/ ps) \/ ch) -> (((ph \/ -. ch) \/ th) -> ((ph \/ ps) \/ th)))

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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