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Metamath Proof Explorer

Theorem shsub1i

Description: Subspace sum is an upper bound of its arguments. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses shincl.1 ⊢ A ∈ S ℋ
shincl.2 ⊢ B ∈ S ℋ
Assertion shsub1i ⊢ A ⊆ A + ℋ B

Proof

Step Hyp Ref Expression
1 shincl.1 ⊢ A ∈ S ℋ
2 shincl.2 ⊢ B ∈ S ℋ
3 1 2 shsel1i ⊢ x ∈ A → x ∈ A + ℋ B
4 3 ssriv ⊢ A ⊆ A + ℋ B