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Metamath Proof Explorer

Theorem chsleji

Description: Subspace sum is smaller than subspace join. Remark in Kalmbach p. 65. (Contributed by NM, 17-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 ⊢ A ∈ C ℋ
chjcl.2 ⊢ B ∈ C ℋ
Assertion chsleji ⊢ A + ℋ B ⊆ A ∨ ℋ B

Proof

Step Hyp Ref Expression
1 ch0le.1 ⊢ A ∈ C ℋ
2 chjcl.2 ⊢ B ∈ C ℋ
3 1 chshii ⊢ A ∈ S ℋ
4 2 chshii ⊢ B ∈ S ℋ
5 3 4 shsleji ⊢ A + ℋ B ⊆ A ∨ ℋ B