Theorem pm2.8 823

Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)

Assertion

Ref	Expression
pm2.8	|- ((ph \/ ps) -> ((-. ps \/ ch) -> (ph \/ ch)))

Proof of Theorem pm2.8

Step	Hyp	Ref	Expression
1		pm2.53 362	. . 3 |- ((ph \/ ps) -> (-. ph -> ps))
2	1	con1d 116	. 2 |- ((ph \/ ps) -> (-. ps -> ph))
3	2	orim1d 812	1 |- ((ph \/ ps) -> ((-. ps \/ ch) -> (ph \/ ch)))

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)