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Theorem 3anassrs 1163
Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypothesis
Ref Expression
3anassrs.1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
3anassrs ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 3anassrs
StepHypRef Expression
1 3anassrs.1 . . 3 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
213exp2 1159 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
32imp41 345 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by:  ralrimivvva  2452  euotd  4055
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