Theorem s3cl

Description: A length 3 string is a word. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s3cl	|- ( ( A e. X /\ B e. X /\ C e. X ) -> <" A B C "> e. Word X )

Proof

Step	Hyp	Ref	Expression
1		simp1	|- ( ( A e. X /\ B e. X /\ C e. X ) -> A e. X )
2		simp2	|- ( ( A e. X /\ B e. X /\ C e. X ) -> B e. X )
3		simp3	|- ( ( A e. X /\ B e. X /\ C e. X ) -> C e. X )
4	1 2 3	s3cld	|- ( ( A e. X /\ B e. X /\ C e. X ) -> <" A B C "> e. Word X )