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	$$⊢\left(A\in X\wedge B\in X\right)\to ⟨“AB”⟩\in \mathrm{Word}X$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(A\in X\wedge B\in X\right)\to A\in X$$
2		simpr	$$⊢\left(A\in X\wedge B\in X\right)\to B\in X$$
3	1 2	s2cld	$$⊢\left(A\in X\wedge B\in X\right)\to ⟨“AB”⟩\in \mathrm{Word}X$$