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Theorem 3anandirs 1602
 Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.)
Hypothesis
Ref Expression
3anandirs.1 (((𝜑𝜃) ∧ (𝜓𝜃) ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
3anandirs (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 3anandirs
StepHypRef Expression
1 simpl1 1248 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
2 simpr 479 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜃)
3 simpl2 1250 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
4 simpl3 1252 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
5 3anandirs.1 . 2 (((𝜑𝜃) ∧ (𝜓𝜃) ∧ (𝜒𝜃)) → 𝜏)
61, 2, 3, 2, 4, 2, 5syl222anc 1511 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 386   ∧ w3a 1113 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 199  df-an 387  df-3an 1115 This theorem is referenced by:  leoptr  29551
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