Theorem s1cl

Description: A singleton word is a word. (Contributed by Stefan O'Rear, 15-Aug-2015) (Revised by Mario Carneiro, 26-Feb-2016) (Proof shortened by AV, 23-Nov-2018)

	Ref	Expression
Assertion	s1cl	⊢ ( 𝐴 ∈ 𝐵 → ⟨“ 𝐴 ”⟩ ∈ Word 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		s1val	⊢ ( 𝐴 ∈ 𝐵 → ⟨“ 𝐴 ”⟩ = { ⟨ 0 , 𝐴 ⟩ } )
2		snopiswrd	⊢ ( 𝐴 ∈ 𝐵 → { ⟨ 0 , 𝐴 ⟩ } ∈ Word 𝐵 )
3	1 2	eqeltrd	⊢ ( 𝐴 ∈ 𝐵 → ⟨“ 𝐴 ”⟩ ∈ Word 𝐵 )