Theorem s8cld

Description: A length 7 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 )
	s5cld.5	|- ( ph -> E e. X )
	s6cld.6	|- ( ph -> F e. X )
	s7cld.7	|- ( ph -> G e. X )
	s8cld.8	|- ( ph -> H e. X )
Assertion	s8cld	|- ( ph -> <" A B C D E F G H "> 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		s5cld.5	|- ( ph -> E e. X )
6		s6cld.6	|- ( ph -> F e. X )
7		s7cld.7	|- ( ph -> G e. X )
8		s8cld.8	|- ( ph -> H e. X )
9		df-s8	|- <" A B C D E F G H "> = ( <" A B C D E F G "> ++ <" H "> )
10	1 2 3 4 5 6 7	s7cld	|- ( ph -> <" A B C D E F G "> e. Word X )
11	9 10 8	cats1cld	|- ( ph -> <" A B C D E F G H "> e. Word X )