Theorem nnaword2

Description: Weak ordering property of addition. (Contributed by NM, 9-Nov-2002)

	Ref	Expression
Assertion	nnaword2	⊢ ( ( 𝐴 ∈ ω ∧ 𝐵 ∈ ω ) → 𝐴 ⊆ ( 𝐵 +o 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		nnaword1	⊢ ( ( 𝐴 ∈ ω ∧ 𝐵 ∈ ω ) → 𝐴 ⊆ ( 𝐴 +o 𝐵 ) )
2		nnacom	⊢ ( ( 𝐴 ∈ ω ∧ 𝐵 ∈ ω ) → ( 𝐴 +o 𝐵 ) = ( 𝐵 +o 𝐴 ) )
3	1 2	sseqtrd	⊢ ( ( 𝐴 ∈ ω ∧ 𝐵 ∈ ω ) → 𝐴 ⊆ ( 𝐵 +o 𝐴 ) )