Theorem naddcl

Description: Closure law for natural addition. (Contributed by Scott Fenton, 26-Aug-2024)

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

Proof

Step	Hyp	Ref	Expression
1		naddcllem	Could not format ( ( A e. On /\ B e. On ) -> ( ( A +no B ) e. On /\ ( A +no B ) = |^| { x e. On | ( ( +no " ( { A } X. B ) ) C_ x /\ ( +no " ( A X. { B } ) ) C_ x ) } ) ) : No typesetting found for |- ( ( A e. On /\ B e. On ) -> ( ( A +no B ) e. On /\ ( A +no B ) = |^| { x e. On | ( ( +no " ( { A } X. B ) ) C_ x /\ ( +no " ( A X. { B } ) ) C_ x ) } ) ) with typecode |-
2	1	simpld	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 |-