Theorem s4cld

Description: A length 4 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 )
	s4cld.4	|- ( ph -> D e. X )
Assertion	s4cld	|- ( ph -> <" A B C D "> 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		s4cld.4	|- ( ph -> D e. X )
5		df-s4	|- <" A B C D "> = ( <" A B C "> ++ <" D "> )
6	1 2 3	s3cld	|- ( ph -> <" A B C "> e. Word X )
7	5 6 4	cats1cld	|- ( ph -> <" A B C D "> e. Word X )