Theorem pm3.48 878

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 400	. . 3 |- ( ps -> ( ps \/ th ) )
2	1	imim2i 16	. 2 |- ( ( ph -> ps ) -> ( ph -> ( ps \/ th ) ) )
3		olc 399	. . 3 |- ( th -> ( ps \/ th ) )
4	3	imim2i 16	. 2 |- ( ( ch -> th ) -> ( ch -> ( ps \/ th ) ) )
5	2, 4	jaao 531	1 |- ( ( ( ph -> ps ) /\ ( ch -> th ) ) -> ( ( ph \/ ch ) -> ( ps \/ th ) ) )

Syntax hints:   -> wi 4   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  orim12d  883  tz7.48lem  7536  caubnd  14098