Theorem naddword2

Description: Weak-ordering principle for natural addition. (Contributed by Scott Fenton, 15-Feb-2025)

	Ref	Expression
Assertion	naddword2	|- ( ( A e. On /\ B e. On ) -> A C_ ( B +no A ) )

Proof

Step	Hyp	Ref	Expression
1		naddword1	|- ( ( A e. On /\ B e. On ) -> A C_ ( A +no B ) )
2		naddcom	|- ( ( A e. On /\ B e. On ) -> ( A +no B ) = ( B +no A ) )
3	1 2	sseqtrd	|- ( ( A e. On /\ B e. On ) -> A C_ ( B +no A ) )