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Theorem pm2.61dda 813
 Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013.)
Hypotheses
Ref Expression
pm2.61dda.1 ((𝜑 ∧ ¬ 𝜓) → 𝜃)
pm2.61dda.2 ((𝜑 ∧ ¬ 𝜒) → 𝜃)
pm2.61dda.3 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
pm2.61dda (𝜑𝜃)

Proof of Theorem pm2.61dda
StepHypRef Expression
1 pm2.61dda.3 . . . 4 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
21anassrs 470 . . 3 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
3 pm2.61dda.2 . . . 4 ((𝜑 ∧ ¬ 𝜒) → 𝜃)
43adantlr 713 . . 3 (((𝜑𝜓) ∧ ¬ 𝜒) → 𝜃)
52, 4pm2.61dan 811 . 2 ((𝜑𝜓) → 𝜃)
6 pm2.61dda.1 . 2 ((𝜑 ∧ ¬ 𝜓) → 𝜃)
75, 6pm2.61dan 811 1 (𝜑𝜃)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 398 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 209  df-an 399 This theorem is referenced by:  lhpexle1lem  37130  lclkrlem2x  38653
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