Theorem nmullid

Description: Identity law for natural multiplication. (Contributed by Scott Fenton, 21-Jul-2026)

	Ref	Expression
Assertion	nmullid	⊢ ( 𝐴 ∈ On → ( 1o ·no 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		1on	⊢ 1o ∈ On
2		nmulcom	⊢ ( ( 1o ∈ On ∧ 𝐴 ∈ On ) → ( 1o ·no 𝐴 ) = ( 𝐴 ·no 1o ) )
3	1 2	mpan	⊢ ( 𝐴 ∈ On → ( 1o ·no 𝐴 ) = ( 𝐴 ·no 1o ) )
4		nmulrid	⊢ ( 𝐴 ∈ On → ( 𝐴 ·no 1o ) = 𝐴 )
5	3 4	eqtrd	⊢ ( 𝐴 ∈ On → ( 1o ·no 𝐴 ) = 𝐴 )