Theorem assintopasslaw

Description: The associative low holds for a associative (closed internal binary) operation for a set. (Contributed by FL, 2-Nov-2009) (Revised by AV, 20-Jan-2020)

	Ref	Expression
Assertion	assintopasslaw	⊢ ( ⚬ ∈ ( assIntOp ‘ 𝑀 ) → ⚬ assLaw 𝑀 )

Proof

Step	Hyp	Ref	Expression
1		assintop	⊢ ( ⚬ ∈ ( assIntOp ‘ 𝑀 ) → ( ⚬ : ( 𝑀 × 𝑀 ) ⟶ 𝑀 ∧ ⚬ assLaw 𝑀 ) )
2	1	simprd	⊢ ( ⚬ ∈ ( assIntOp ‘ 𝑀 ) → ⚬ assLaw 𝑀 )