Theorem s2cld

Description: A doubleton word is a word. (Contributed by Mario Carneiro, 27-Feb-2016)

	Ref	Expression
Hypotheses	s2cld.1	$$⊢\phi \to A\in X$$
	s2cld.2	$$⊢\phi \to B\in X$$
Assertion	s2cld	$$⊢\phi \to ⟨“AB”⟩\in \mathrm{Word}X$$

Proof

Step	Hyp	Ref	Expression
1		s2cld.1	$$⊢\phi \to A\in X$$
2		s2cld.2	$$⊢\phi \to B\in X$$
3		df-s2	$$⊢⟨“AB”⟩=⟨“A”⟩\mathrm{++}⟨“B”⟩$$
4	1	s1cld	$$⊢\phi \to ⟨“A”⟩\in \mathrm{Word}X$$
5	3 4 2	cats1cld	$$⊢\phi \to ⟨“AB”⟩\in \mathrm{Word}X$$