Theorem orim12i 754

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 728	. 2 |- ( ph -> ( ps \/ th ) )
3		orim12i.2	. . 3 |- ( ch -> th )
4	3	olcd 729	. 2 |- ( ch -> ( ps \/ th ) )
5	2, 4	jaoi 711	1 |- ( ( ph \/ ch ) -> ( ps \/ th ) )

Syntax hints:   -> wi 4   \/ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  orim1i  755  orim2i  756  dcim  836  pm5.12dc  905  pm5.14dc  906  pm5.55dc  908  pm5.54dc  913  prlem2  969  xordc1  1388  19.43  1621  eueq3dc  2904  inssun  3367  abvor0dc  3438  ifmdc  3565  undifexmid  4179  pwssunim  4269  ordtriexmid  4505  ontriexmidim  4506  ordtri2orexmid  4507  ontr2exmid  4509  onsucsssucexmid  4511  onsucelsucexmid  4514  ordsoexmid  4546  0elsucexmid  4549  ordpwsucexmid  4554  ordtri2or2exmid  4555  ontri2orexmidim  4556  funcnvuni  5267  oprabidlem  5884  2oconcl  6418  inffiexmid  6884  unfiexmid  6895  ctssexmid  7126  exmidonfinlem  7170  sup3exmid  8873  zeo  9317  ef0lem  11623