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

Step	Hyp	Ref	Expression
1		3anassrs.1	. . 3 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)
2	1	3exp2 1169	. 2 ⊢ (φ → (ψ → (χ → (θ → τ))))
3	2	imp41 576	1 ⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → τ)

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)