Theorem nmull0d

Description: Natural multiplication by zero. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

	Ref	Expression
Hypothesis	nmul.1	⊢ ( 𝜑 → 𝐴 ∈ On )
Assertion	nmull0d	⊢ ( 𝜑 → ( ∅ ·no 𝐴 ) = ∅ )

Proof

Step	Hyp	Ref	Expression
1		nmul.1	⊢ ( 𝜑 → 𝐴 ∈ On )
2		nmull0	⊢ ( 𝐴 ∈ On → ( ∅ ·no 𝐴 ) = ∅ )
3	1 2	syl	⊢ ( 𝜑 → ( ∅ ·no 𝐴 ) = ∅ )