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Theorem orim12i 502
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 ((φ χ) → (ψ θ))

Proof of Theorem orim12i
StepHypRef Expression
1 orim12i.1 . . 3 (φψ)
21orcd 381 . 2 (φ → (ψ θ))
3 orim12i.2 . . 3 (χθ)
43olcd 382 . 2 (χ → (ψ θ))
52, 4jaoi 368 1 ((φ χ) → (ψ θ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wo 357
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 177  df-or 359
This theorem is referenced by:  orim1i  503  orim2i  504  prlem2  929  eueq3  3011  lefinlteq  4463  funcnvuni  5161  muc0or  6252  nchoicelem9  6297
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