Theorem orim12i 502

Description: Disjoin antecedents and consequents of two premises. (Contributed by NM, 6-Jun-1994.) (Proof shortened by Wolf Lammen, 25-Jul-2012.)

Hypotheses

Ref	Expression
orim12i.1	|- (ph -> ps)
orim12i.2	|- (ch -> th)

Assertion

Ref	Expression
orim12i	|- ((ph \/ ch) -> (ps \/ th))

Proof of Theorem orim12i

Step	Hyp	Ref	Expression
1		orim12i.1	. . 3 |- (ph -> ps)
2	1	orcd 381	. 2 |- (ph -> (ps \/ th))
3		orim12i.2	. . 3 |- (ch -> th)
4	3	olcd 382	. 2 |- (ch -> (ps \/ th))
5	2, 4	jaoi 368	1 |- ((ph \/ ch) -> (ps \/ th))

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

This theorem is referenced by:  orim1i  503  orim2i  504  prlem2  929  eueq3  3012  lefinlteq  4464  funcnvuni  5162  muc0or  6253  nchoicelem9  6298