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  4238  pwssunim  4332  ordtriexmid  4570  ontriexmidim  4571  ordtri2orexmid  4572  ontr2exmid  4574  onsucsssucexmid  4576  onsucelsucexmid  4579  ordsoexmid  4611  0elsucexmid  4614  ordpwsucexmid  4619  ordtri2or2exmid  4620  ontri2orexmidim  4621  funcnvuni  5344  oprabidlem  5977  2oconcl  6527  inffiexmid  7005  unfiexmid  7017  ctssexmid  7254  exmidonfinlem  7303  sup3exmid  9032  zeo  9480  ef0lem  12004