Theorem anass1rs

Description: Commutative-associative law for conjunction in an antecedent. (Contributed by Jeff Madsen, 19-Jun-2011)

	Ref	Expression
Hypothesis	anass1rs.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	anass1rs	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		anass1rs.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2	1	anassrs	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3	2	an32s	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) → 𝜃 )