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Theorem 3anandirs 1252
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.)
Hypothesis
Ref Expression
3anandirs.1 (((𝜑𝜃) ∧ (𝜓𝜃) ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
3anandirs (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 3anandirs
StepHypRef Expression
1 simpl1 916 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
2 simpr 107 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜃)
3 simpl2 917 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
4 simpl3 918 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
5 3anandirs.1 . 2 (((𝜑𝜃) ∧ (𝜓𝜃) ∧ (𝜒𝜃)) → 𝜏)
61, 2, 3, 2, 4, 2, 5syl222anc 1160 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 894
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 896
This theorem is referenced by: (None)
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