Theorem pm3.48 785

Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) (Revised by NM, 1-Dec-2012.)

Assertion

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

Proof of Theorem pm3.48

Step	Hyp	Ref	Expression
1		orc 712	. . 3 |- ( ps -> ( ps \/ th ) )
2	1	imim2i 12	. 2 |- ( ( ph -> ps ) -> ( ph -> ( ps \/ th ) ) )
3		olc 711	. . 3 |- ( th -> ( ps \/ th ) )
4	3	imim2i 12	. 2 |- ( ( ch -> th ) -> ( ch -> ( ps \/ th ) ) )
5	2, 4	jaao 719	1 |- ( ( ( ph -> ps ) /\ ( ch -> th ) ) -> ( ( ph \/ ch ) -> ( ps \/ th ) ) )

Syntax hints:   -> wi 4   /\ wa 104   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim12d  786