Theorem pm3.48 806

Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.)

Assertion

Ref	Expression
pm3.48	|- (((ph -> ps) /\ (ch -> th)) -> ((ph \/ ch) -> (ps \/ th)))

Proof of Theorem pm3.48

Step	Hyp	Ref	Expression
1		orc 374	. . 3 |- (ps -> (ps \/ th))
2	1	imim2i 13	. 2 |- ((ph -> ps) -> (ph -> (ps \/ th)))
3		olc 373	. . 3 |- (th -> (ps \/ th))
4	3	imim2i 13	. 2 |- ((ch -> th) -> (ch -> (ps \/ th)))
5	2, 4	jaao 495	1 |- (((ph -> ps) /\ (ch -> th)) -> ((ph \/ ch) -> (ps \/ th)))

Syntax hints:   -> wi 4   \/ wo 357   /\ wa 358

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:  orim12d  811