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Theorem orim12d 811
 Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.)
Hypotheses
Ref Expression
orim12d.1 (φ → (ψχ))
orim12d.2 (φ → (θτ))
Assertion
Ref Expression
orim12d (φ → ((ψ θ) → (χ τ)))

Proof of Theorem orim12d
StepHypRef Expression
1 orim12d.1 . 2 (φ → (ψχ))
2 orim12d.2 . 2 (φ → (θτ))
3 pm3.48 806 . 2 (((ψχ) (θτ)) → ((ψ θ) → (χ τ)))
41, 2, 3syl2anc 642 1 (φ → ((ψ θ) → (χ τ)))
 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  df-an 360 This theorem is referenced by:  orim1d  812  orim2d  813  3orim123d  1260  preq12b  4127  evenoddnnnul  4514  funun  5146  enprmaplem3  6078  leconnnc  6218  nchoicelem9  6297  nchoicelem17  6305
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