Step |
Hyp |
Ref |
Expression |
1 |
|
evpmval.1 |
|- A = ( pmEven ` D ) |
2 |
|
elex |
|- ( D e. V -> D e. _V ) |
3 |
|
fveq2 |
|- ( d = D -> ( pmSgn ` d ) = ( pmSgn ` D ) ) |
4 |
3
|
cnveqd |
|- ( d = D -> `' ( pmSgn ` d ) = `' ( pmSgn ` D ) ) |
5 |
4
|
imaeq1d |
|- ( d = D -> ( `' ( pmSgn ` d ) " { 1 } ) = ( `' ( pmSgn ` D ) " { 1 } ) ) |
6 |
|
df-evpm |
|- pmEven = ( d e. _V |-> ( `' ( pmSgn ` d ) " { 1 } ) ) |
7 |
|
fvex |
|- ( pmSgn ` D ) e. _V |
8 |
7
|
cnvex |
|- `' ( pmSgn ` D ) e. _V |
9 |
8
|
imaex |
|- ( `' ( pmSgn ` D ) " { 1 } ) e. _V |
10 |
5 6 9
|
fvmpt |
|- ( D e. _V -> ( pmEven ` D ) = ( `' ( pmSgn ` D ) " { 1 } ) ) |
11 |
2 10
|
syl |
|- ( D e. V -> ( pmEven ` D ) = ( `' ( pmSgn ` D ) " { 1 } ) ) |
12 |
1 11
|
syl5eq |
|- ( D e. V -> A = ( `' ( pmSgn ` D ) " { 1 } ) ) |