Theorem orim12i 761

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 735	. 2 |- ( ph -> ( ps \/ th ) )
3		orim12i.2	. . 3 |- ( ch -> th )
4	3	olcd 736	. 2 |- ( ch -> ( ps \/ th ) )
5	2, 4	jaoi 718	1 |- ( ( ph \/ ch ) -> ( ps \/ th ) )

Syntax hints:   -> wi 4   \/ wo 710

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 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim1i  762  orim2i  763  dcim  843  pm5.12dc  912  pm5.14dc  913  pm5.55dc  915  pm5.54dc  920  prlem2  977  xordc1  1413  19.43  1652  eueq3dc  2954  inssun  3421  abvor0dc  3492  ifmdc  3622  undifexmid  4253  pwssunim  4349  ordtriexmid  4587  ontriexmidim  4588  ordtri2orexmid  4589  ontr2exmid  4591  onsucsssucexmid  4593  onsucelsucexmid  4596  ordsoexmid  4628  0elsucexmid  4631  ordpwsucexmid  4636  ordtri2or2exmid  4637  ontri2orexmidim  4638  funcnvuni  5362  oprabidlem  5998  2oconcl  6548  inffiexmid  7029  unfiexmid  7041  ctssexmid  7278  exmidonfinlem  7332  sup3exmid  9065  zeo  9513  ef0lem  12086