Step |
Hyp |
Ref |
Expression |
1 |
|
efgmval.m |
|- M = ( y e. I , z e. 2o |-> <. y , ( 1o \ z ) >. ) |
2 |
|
opeq1 |
|- ( a = A -> <. a , ( 1o \ b ) >. = <. A , ( 1o \ b ) >. ) |
3 |
|
difeq2 |
|- ( b = B -> ( 1o \ b ) = ( 1o \ B ) ) |
4 |
3
|
opeq2d |
|- ( b = B -> <. A , ( 1o \ b ) >. = <. A , ( 1o \ B ) >. ) |
5 |
|
opeq1 |
|- ( y = a -> <. y , ( 1o \ z ) >. = <. a , ( 1o \ z ) >. ) |
6 |
|
difeq2 |
|- ( z = b -> ( 1o \ z ) = ( 1o \ b ) ) |
7 |
6
|
opeq2d |
|- ( z = b -> <. a , ( 1o \ z ) >. = <. a , ( 1o \ b ) >. ) |
8 |
5 7
|
cbvmpov |
|- ( y e. I , z e. 2o |-> <. y , ( 1o \ z ) >. ) = ( a e. I , b e. 2o |-> <. a , ( 1o \ b ) >. ) |
9 |
1 8
|
eqtri |
|- M = ( a e. I , b e. 2o |-> <. a , ( 1o \ b ) >. ) |
10 |
|
opex |
|- <. A , ( 1o \ B ) >. e. _V |
11 |
2 4 9 10
|
ovmpo |
|- ( ( A e. I /\ B e. 2o ) -> ( A M B ) = <. A , ( 1o \ B ) >. ) |