Metamath Proof Explorer


Theorem s2cl

Description: A doubleton word is a word. (Contributed by Stefan O'Rear, 23-Aug-2015) (Revised by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion s2cl ⊢ A ∈ X ∧ B ∈ X → ⟨“ AB ”⟩ ∈ Word X

Proof

Step Hyp Ref Expression
1 simpl ⊢ A ∈ X ∧ B ∈ X → A ∈ X
2 simpr ⊢ A ∈ X ∧ B ∈ X → B ∈ X
3 1 2 s2cld ⊢ A ∈ X ∧ B ∈ X → ⟨“ AB ”⟩ ∈ Word X