Theorem orim12i 764

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 738	. 2 |- ( ph -> ( ps \/ th ) )
3		orim12i.2	. . 3 |- ( ch -> th )
4	3	olcd 739	. 2 |- ( ch -> ( ps \/ th ) )
5	2, 4	jaoi 721	1 |- ( ( ph \/ ch ) -> ( ps \/ th ) )

Syntax hints:   -> wi 4   \/ wo 713

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 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim1i  765  orim2i  766  dcim  846  pm5.12dc  915  pm5.14dc  916  pm5.55dc  918  pm5.54dc  923  prlem2  980  ifpdc  985  ifpor  993  xordc1  1435  19.43  1674  eueq3dc  2978  inssun  3445  abvor0dc  3516  ifmdc  3646  undifexmid  4281  pwssunim  4379  ordtriexmid  4617  ontriexmidim  4618  ordtri2orexmid  4619  ontr2exmid  4621  onsucsssucexmid  4623  onsucelsucexmid  4626  ordsoexmid  4658  0elsucexmid  4661  ordpwsucexmid  4666  ordtri2or2exmid  4667  ontri2orexmidim  4668  funcnvuni  5396  oprabidlem  6044  2oconcl  6602  inffiexmid  7093  unfiexmid  7105  ctssexmid  7343  exmidonfinlem  7397  sup3exmid  9130  zeo  9578  ef0lem  12214