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	$$⊢A\in B\to ⟨“A”⟩\in \mathrm{Word}B$$

Proof

Step	Hyp	Ref	Expression
1		s1val	$$⊢A\in B\to ⟨“A”⟩=\left\{⟨0,A⟩\right\}$$
2		snopiswrd	$$⊢A\in B\to \left\{⟨0,A⟩\right\}\in \mathrm{Word}B$$
3	1 2	eqeltrd	$$⊢A\in B\to ⟨“A”⟩\in \mathrm{Word}B$$