Theorem s3cld

Description: A length 3 string 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 )
	s3cld.3	|- ( ph -> C e. X )
Assertion	s3cld	|- ( ph -> <" A B C "> e. Word X )

Proof

Step	Hyp	Ref	Expression
1		s2cld.1	|- ( ph -> A e. X )
2		s2cld.2	|- ( ph -> B e. X )
3		s3cld.3	|- ( ph -> C e. X )
4		df-s3	|- <" A B C "> = ( <" A B "> ++ <" C "> )
5	1 2	s2cld	|- ( ph -> <" A B "> e. Word X )
6	4 5 3	cats1cld	|- ( ph -> <" A B C "> e. Word X )