Theorem orim12i 767

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 741	. 2 |- ( ph -> ( ps \/ th ) )
3		orim12i.2	. . 3 |- ( ch -> th )
4	3	olcd 742	. 2 |- ( ch -> ( ps \/ th ) )
5	2, 4	jaoi 724	1 |- ( ( ph \/ ch ) -> ( ps \/ th ) )

Syntax hints:   -> wi 4   \/ wo 716

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 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim1i  768  orim2i  769  dcim  849  pm5.12dc  918  pm5.14dc  919  pm5.55dc  921  pm5.54dc  926  prlem2  983  ifpdc  988  ifpor  996  xordc1  1438  19.43  1677  eueq3dc  2993  inssun  3463  abvor0dc  3534  ifmdc  3667  undifexmid  4308  pwssunim  4407  ordtriexmid  4645  ontriexmidim  4646  ordtri2orexmid  4647  ontr2exmid  4649  onsucsssucexmid  4651  onsucelsucexmid  4654  ordsoexmid  4686  0elsucexmid  4689  ordpwsucexmid  4694  ordtri2or2exmid  4695  ontri2orexmidim  4696  funcnvuni  5427  oprabidlem  6083  2oconcl  6674  inffiexmid  7168  unfiexmid  7180  ctssexmid  7443  exmidonfinlem  7498  sup3exmid  9236  zeo  9689  ef0lem  12354