Theorem nmullidd

Description: Identity law for natural multiplication. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

	Ref	Expression
Hypothesis	nmul.1	⊢ ( 𝜑 → 𝐴 ∈ On )
Assertion	nmullidd	⊢ ( 𝜑 → ( 1o ·no 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nmul.1	⊢ ( 𝜑 → 𝐴 ∈ On )
2		nmullid	⊢ ( 𝐴 ∈ On → ( 1o ·no 𝐴 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 1o ·no 𝐴 ) = 𝐴 )