Theorem pm2.82 825

Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

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 6	. . 3 |- ((ph \/ ps) -> ((ph \/ -. ch) -> (ph \/ ps)))
2		pm2.24 101	. . . 4 |- (ch -> (-. ch -> ps))
3	2	orim2d 813	. . 3 |- (ch -> ((ph \/ -. ch) -> (ph \/ ps)))
4	1, 3	jaoi 368	. 2 |- (((ph \/ ps) \/ ch) -> ((ph \/ -. ch) -> (ph \/ ps)))
5	4	orim1d 812	1 |- (((ph \/ ps) \/ ch) -> (((ph \/ -. ch) \/ th) -> ((ph \/ ps) \/ th)))

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by: (None)