Theorem nmull0

Description: Natural multiplication by zero. (Contributed by Scott Fenton, 10-Jun-2026)

	Ref	Expression
Assertion	nmull0	Could not format assertion : No typesetting found for |- ( A e. On -> ( (/) .no A ) = (/) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		0elon	$$⊢\varnothing \in \mathrm{On}$$
2		nmulcom	Could not format ( ( A e. On /\ (/) e. On ) -> ( A .no (/) ) = ( (/) .no A ) ) : No typesetting found for |- ( ( A e. On /\ (/) e. On ) -> ( A .no (/) ) = ( (/) .no A ) ) with typecode |-
3	1 2	mpan2	Could not format ( A e. On -> ( A .no (/) ) = ( (/) .no A ) ) : No typesetting found for |- ( A e. On -> ( A .no (/) ) = ( (/) .no A ) ) with typecode |-
4		nmulr0	Could not format ( A e. On -> ( A .no (/) ) = (/) ) : No typesetting found for |- ( A e. On -> ( A .no (/) ) = (/) ) with typecode |-
5	3 4	eqtr3d	Could not format ( A e. On -> ( (/) .no A ) = (/) ) : No typesetting found for |- ( A e. On -> ( (/) .no A ) = (/) ) with typecode |-