Theorem 3anassrs

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017)

	Ref	Expression
Hypothesis	3anassrs.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion	3anassrs	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

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