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Theorem 3anandis 1308
 Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 18-Apr-2007.)
Hypothesis
Ref Expression
3anandis.1 (((𝜑𝜓) ∧ (𝜑𝜒) ∧ (𝜑𝜃)) → 𝜏)
Assertion
Ref Expression
3anandis ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)

Proof of Theorem 3anandis
StepHypRef Expression
1 simpl 108 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜑)
2 simpr1 970 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)
3 simpr2 971 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)
4 simpr3 972 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)
5 3anandis.1 . 2 (((𝜑𝜓) ∧ (𝜑𝜒) ∧ (𝜑𝜃)) → 𝜏)
61, 2, 1, 3, 1, 4, 5syl222anc 1215 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 945 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 947 This theorem is referenced by: (None)
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