Theorem naddlid

Description: Ordinal zero is the additive identity for natural addition. (Contributed by Scott Fenton, 20-Feb-2025)

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

Proof

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