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  1651  eueq3dc  2947  inssun  3413  abvor0dc  3484  ifmdc  3612  undifexmid  4237  pwssunim  4331  ordtriexmid  4569  ontriexmidim  4570  ordtri2orexmid  4571  ontr2exmid  4573  onsucsssucexmid  4575  onsucelsucexmid  4578  ordsoexmid  4610  0elsucexmid  4613  ordpwsucexmid  4618  ordtri2or2exmid  4619  ontri2orexmidim  4620  funcnvuni  5343  oprabidlem  5975  2oconcl  6525  inffiexmid  7003  unfiexmid  7015  ctssexmid  7252  exmidonfinlem  7301  sup3exmid  9030  zeo  9478  ef0lem  11971