Theorem nmulcld

Description: Closure law for natrual multiplication. Deduction form. (Contributed by Scott Fenton, 12-Jun-2026)

	Ref	Expression
Hypotheses	nmulcld.1	$$⊢\phi \to A\in \mathrm{On}$$
	nmulcld.2	$$⊢\phi \to B\in \mathrm{On}$$
Assertion	nmulcld	Could not format assertion : No typesetting found for |- ( ph -> ( A .no B ) e. On ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		nmulcld.1	$$⊢\phi \to A\in \mathrm{On}$$
2		nmulcld.2	$$⊢\phi \to B\in \mathrm{On}$$
3		nmulcl	Could not format ( ( A e. On /\ B e. On ) -> ( A .no B ) e. On ) : No typesetting found for |- ( ( A e. On /\ B e. On ) -> ( A .no B ) e. On ) with typecode |-
4	1 2 3	syl2anc	Could not format ( ph -> ( A .no B ) e. On ) : No typesetting found for |- ( ph -> ( A .no B ) e. On ) with typecode |-