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Theorem orim12i 908
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 (𝜑𝜓)
orim12i.2 (𝜒𝜃)
Assertion
Ref Expression
orim12i ((𝜑𝜒) → (𝜓𝜃))

Proof of Theorem orim12i
StepHypRef Expression
1 orim12i.1 . . 3 (𝜑𝜓)
21orcd 872 . 2 (𝜑 → (𝜓𝜃))
3 orim12i.2 . . 3 (𝜒𝜃)
43olcd 873 . 2 (𝜒 → (𝜓𝜃))
52, 4jaoi 856 1 ((𝜑𝜒) → (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 846
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-or 847
This theorem is referenced by:  orim1i  909  orim2i  910  prlem2  1055  ifpor  1072  eueq3  3674  pwssun  5533  xpima  6139  fvresval  7308  0mpo0  7445  funcnvuni  7873  2oconcl  8454  djur  9862  djuun  9869  fin23lem23  10269  fin23lem19  10279  fin1a2lem13  10355  fin1a2s  10357  nn0ge0  12445  elfzlmr  13693  hash2pwpr  14382  trclfvg  14907  xpcbas  18073  odcl  19325  gexcl  19369  ang180lem4  26178  sltn0  27256  elim2ifim  31509  locfinref  32462  volmeas  32870  nepss  34329  funpsstri  34379  bj-prmoore  35615  bj-imdirco  35690  dvasin  36191  dvacos  36192  disjorimxrn  37239  relexpxpmin  42063  clsk1indlem3  42389  elsprel  45741  resolution  47320
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