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Theorem 3anandirs 1468
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 1187 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
2 simpr 487 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜃)
3 simpl2 1188 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
4 simpl3 1189 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
5 3anandirs.1 . 2 (((𝜑𝜃) ∧ (𝜓𝜃) ∧ (𝜒𝜃)) → 𝜏)
61, 2, 3, 2, 4, 2, 5syl222anc 1382 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1083
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  df-3an 1085
This theorem is referenced by:  leoptr  29899
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