Theorem orim12d 811

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.)

Hypotheses

Ref	Expression
orim12d.1	|- (ph -> (ps -> ch))
orim12d.2	|- (ph -> (th -> ta))

Assertion

Ref	Expression
orim12d	|- (ph -> ((ps \/ th) -> (ch \/ ta)))

Proof of Theorem orim12d

Step	Hyp	Ref	Expression
1		orim12d.1	. 2 |- (ph -> (ps -> ch))
2		orim12d.2	. 2 |- (ph -> (th -> ta))
3		pm3.48 806	. 2 |- (((ps -> ch) /\ (th -> ta)) -> ((ps \/ th) -> (ch \/ ta)))
4	1, 2, 3	syl2anc 642	1 |- (ph -> ((ps \/ th) -> (ch \/ ta)))

Syntax hints:   -> 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:  orim1d  812  orim2d  813  3orim123d  1260  preq12b  4127  evenoddnnnul  4514  funun  5146  enprmaplem3  6078  leconnnc  6218  nchoicelem9  6297  nchoicelem17  6305