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Metamath Proof Explorer

Theorem hvsubcli

Description: Closure of vector subtraction. (Contributed by NM, 2-Aug-1999) (New usage is discouraged.)

Ref Expression
Hypotheses hvaddcl.1 ⊢ A ∈ ℋ
hvaddcl.2 ⊢ B ∈ ℋ
Assertion hvsubcli ⊢ A - ℎ B ∈ ℋ

Proof

Step Hyp Ref Expression
1 hvaddcl.1 ⊢ A ∈ ℋ
2 hvaddcl.2 ⊢ B ∈ ℋ
3 hvsubcl ⊢ A ∈ ℋ ∧ B ∈ ℋ → A - ℎ B ∈ ℋ
4 1 2 3 mp2an ⊢ A - ℎ B ∈ ℋ