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Theorem pm2.61ddan 828
Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013.)
Hypotheses
Ref Expression
pm2.61ddan.1 ((𝜑𝜓) → 𝜃)
pm2.61ddan.2 ((𝜑𝜒) → 𝜃)
pm2.61ddan.3 ((𝜑 ∧ (¬ 𝜓 ∧ ¬ 𝜒)) → 𝜃)
Assertion
Ref Expression
pm2.61ddan (𝜑𝜃)

Proof of Theorem pm2.61ddan
StepHypRef Expression
1 pm2.61ddan.1 . 2 ((𝜑𝜓) → 𝜃)
2 pm2.61ddan.2 . . . 4 ((𝜑𝜒) → 𝜃)
32adantlr 746 . . 3 (((𝜑 ∧ ¬ 𝜓) ∧ 𝜒) → 𝜃)
4 pm2.61ddan.3 . . . 4 ((𝜑 ∧ (¬ 𝜓 ∧ ¬ 𝜒)) → 𝜃)
54anassrs 677 . . 3 (((𝜑 ∧ ¬ 𝜓) ∧ ¬ 𝜒) → 𝜃)
63, 5pm2.61dan 827 . 2 ((𝜑 ∧ ¬ 𝜓) → 𝜃)
71, 6pm2.61dan 827 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  lgsdir2  24799  cdlemg24  34777
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