Theorem orim12i 764

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	⊢ (𝜑 → 𝜓)
orim12i.2	⊢ (𝜒 → 𝜃)

Assertion

Ref	Expression
orim12i	⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))

Proof of Theorem orim12i

Step	Hyp	Ref	Expression
1		orim12i.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	orcd 738	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜃))
3		orim12i.2	. . 3 ⊢ (𝜒 → 𝜃)
4	3	olcd 739	. 2 ⊢ (𝜒 → (𝜓 ∨ 𝜃))
5	2, 4	jaoi 721	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))

Syntax hints:   → wi 4   ∨ wo 713

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 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim1i  765  orim2i  766  dcim  846  pm5.12dc  915  pm5.14dc  916  pm5.55dc  918  pm5.54dc  923  prlem2  980  ifpdc  985  ifpor  993  xordc1  1435  19.43  1674  eueq3dc  2977  inssun  3444  abvor0dc  3515  ifmdc  3645  undifexmid  4278  pwssunim  4376  ordtriexmid  4614  ontriexmidim  4615  ordtri2orexmid  4616  ontr2exmid  4618  onsucsssucexmid  4620  onsucelsucexmid  4623  ordsoexmid  4655  0elsucexmid  4658  ordpwsucexmid  4663  ordtri2or2exmid  4664  ontri2orexmidim  4665  funcnvuni  5393  oprabidlem  6041  2oconcl  6598  inffiexmid  7084  unfiexmid  7096  ctssexmid  7333  exmidonfinlem  7387  sup3exmid  9120  zeo  9568  ef0lem  12192