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  2990  inssun  3460  abvor0dc  3531  ifmdc  3664  undifexmid  4305  pwssunim  4404  ordtriexmid  4642  ontriexmidim  4643  ordtri2orexmid  4644  ontr2exmid  4646  onsucsssucexmid  4648  onsucelsucexmid  4651  ordsoexmid  4683  0elsucexmid  4686  ordpwsucexmid  4691  ordtri2or2exmid  4692  ontri2orexmidim  4693  funcnvuni  5424  oprabidlem  6080  2oconcl  6671  inffiexmid  7165  unfiexmid  7177  ctssexmid  7440  exmidonfinlem  7495  sup3exmid  9227  zeo  9679  ef0lem  12339