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 |
1 2 3 4
|
s4eqd |
|- ( ph -> <" A B C D "> = <" N O P Q "> ) |
7 |
5
|
s1eqd |
|- ( ph -> <" E "> = <" R "> ) |
8 |
6 7
|
oveq12d |
|- ( ph -> ( <" A B C D "> ++ <" E "> ) = ( <" N O P Q "> ++ <" R "> ) ) |
9 |
|
df-s5 |
|- <" A B C D E "> = ( <" A B C D "> ++ <" E "> ) |
10 |
|
df-s5 |
|- <" N O P Q R "> = ( <" N O P Q "> ++ <" R "> ) |
11 |
8 9 10
|
3eqtr4g |
|- ( ph -> <" A B C D E "> = <" N O P Q R "> ) |