Theorem s2cld

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

	Ref	Expression
Hypotheses	s2cld.1	|- ( ph -> A e. X )
	s2cld.2	|- ( ph -> B e. X )
Assertion	s2cld	|- ( ph -> <" A B "> e. Word X )

Proof

Step	Hyp	Ref	Expression
1		s2cld.1	|- ( ph -> A e. X )
2		s2cld.2	|- ( ph -> B e. X )
3		df-s2	|- <" A B "> = ( <" A "> ++ <" B "> )
4	1	s1cld	|- ( ph -> <" A "> e. Word X )
5	3 4 2	cats1cld	|- ( ph -> <" A B "> e. Word X )