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Metamath Proof Explorer

Theorem shsub2i

Description: Subspace sum is an upper bound of its arguments. (Contributed by NM, 17-Dec-2004) (New usage is discouraged.)

Ref Expression
Hypotheses shincl.1 ⊢ A ∈ S ℋ
shincl.2 ⊢ B ∈ S ℋ
Assertion shsub2i ⊢ A ⊆ B + ℋ A

Proof

Step Hyp Ref Expression
1 shincl.1 ⊢ A ∈ S ℋ
2 shincl.2 ⊢ B ∈ S ℋ
3 2 1 shsel2i ⊢ x ∈ A → x ∈ B + ℋ A
4 3 ssriv ⊢ A ⊆ B + ℋ A