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Theorem 3anandis 1583
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 474 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜑)
2 simpr1 1234 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)
3 simpr2 1236 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)
4 simpr3 1238 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)
5 3anandis.1 . 2 (((𝜑𝜓) ∧ (𝜑𝜒) ∧ (𝜑𝜃)) → 𝜏)
61, 2, 1, 3, 1, 4, 5syl222anc 1493 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by: (None)
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