Theorem s7eqd

Description: Equality theorem for a length 7 word. (Contributed by Mario Carneiro, 27-Feb-2016)

	Ref	Expression
Hypotheses	s2eqd.1	|- ( ph -> A = N )
	s2eqd.2	|- ( ph -> B = O )
	s3eqd.3	|- ( ph -> C = P )
	s4eqd.4	|- ( ph -> D = Q )
	s5eqd.5	|- ( ph -> E = R )
	s6eqd.6	|- ( ph -> F = S )
	s7eqd.6	|- ( ph -> G = T )
Assertion	s7eqd	|- ( ph -> <" A B C D E F G "> = <" N O P Q R S T "> )

Proof

Step	Hyp	Ref	Expression
1		s2eqd.1	|- ( ph -> A = N )
2		s2eqd.2	|- ( ph -> B = O )
3		s3eqd.3	|- ( ph -> C = P )
4		s4eqd.4	|- ( ph -> D = Q )
5		s5eqd.5	|- ( ph -> E = R )
6		s6eqd.6	|- ( ph -> F = S )
7		s7eqd.6	|- ( ph -> G = T )
8	1 2 3 4 5 6	s6eqd	|- ( ph -> <" A B C D E F "> = <" N O P Q R S "> )
9	7	s1eqd	|- ( ph -> <" G "> = <" T "> )
10	8 9	oveq12d	|- ( ph -> ( <" A B C D E F "> ++ <" G "> ) = ( <" N O P Q R S "> ++ <" T "> ) )
11		df-s7	|- <" A B C D E F G "> = ( <" A B C D E F "> ++ <" G "> )
12		df-s7	|- <" N O P Q R S T "> = ( <" N O P Q R S "> ++ <" T "> )
13	10 11 12	3eqtr4g	|- ( ph -> <" A B C D E F G "> = <" N O P Q R S T "> )