Theorem hvaddcli

Description: Closure of vector addition. (Contributed by NM, 1-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hvaddcl.1	⊢ 𝐴 ∈ ℋ
	hvaddcl.2	⊢ 𝐵 ∈ ℋ
Assertion	hvaddcli	⊢ ( 𝐴 +ℎ 𝐵 ) ∈ ℋ

Proof

Step	Hyp	Ref	Expression
1		hvaddcl.1	⊢ 𝐴 ∈ ℋ
2		hvaddcl.2	⊢ 𝐵 ∈ ℋ
3		hvaddcl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 +ℎ 𝐵 ) ∈ ℋ )
4	1 2 3	mp2an	⊢ ( 𝐴 +ℎ 𝐵 ) ∈ ℋ