Theorem nmulcomd

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

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

Proof

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