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Theorem 3anassrs 1173
Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypothesis
Ref Expression
3anassrs.1 ((φ (ψ χ θ)) → τ)
Assertion
Ref Expression
3anassrs ((((φ ψ) χ) θ) → τ)

Proof of Theorem 3anassrs
StepHypRef Expression
1 3anassrs.1 . . 3 ((φ (ψ χ θ)) → τ)
213exp2 1169 . 2 (φ → (ψ → (χ → (θτ))))
32imp41 576 1 ((((φ ψ) χ) θ) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
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