Theorem pm5.14 856

Description: Theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.14	|- ((ph -> ps) \/ (ps -> ch))

Proof of Theorem pm5.14

Step	Hyp	Ref	Expression
1		ax-1 6	. . . 4 |- (ps -> (ph -> ps))
2	1	con3i 127	. . 3 |- (-. (ph -> ps) -> -. ps)
3	2	pm2.21d 98	. 2 |- (-. (ph -> ps) -> (ps -> ch))
4	3	orri 365	1 |- ((ph -> ps) \/ (ps -> ch))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   \/ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  pm5.13  857