| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ax-i2m1 |
|- ( ( _i x. _i ) + 1 ) = 0 |
| 2 |
|
1re |
|- 1 e. RR |
| 3 |
|
renegid2 |
|- ( 1 e. RR -> ( ( 0 -R 1 ) + 1 ) = 0 ) |
| 4 |
2 3
|
ax-mp |
|- ( ( 0 -R 1 ) + 1 ) = 0 |
| 5 |
1 4
|
eqtr4i |
|- ( ( _i x. _i ) + 1 ) = ( ( 0 -R 1 ) + 1 ) |
| 6 |
|
ax-icn |
|- _i e. CC |
| 7 |
6 6
|
mulcli |
|- ( _i x. _i ) e. CC |
| 8 |
7
|
a1i |
|- ( T. -> ( _i x. _i ) e. CC ) |
| 9 |
|
rernegcl |
|- ( 1 e. RR -> ( 0 -R 1 ) e. RR ) |
| 10 |
9
|
recnd |
|- ( 1 e. RR -> ( 0 -R 1 ) e. CC ) |
| 11 |
2 10
|
mp1i |
|- ( T. -> ( 0 -R 1 ) e. CC ) |
| 12 |
|
1cnd |
|- ( T. -> 1 e. CC ) |
| 13 |
8 11 12
|
sn-addcan2d |
|- ( T. -> ( ( ( _i x. _i ) + 1 ) = ( ( 0 -R 1 ) + 1 ) <-> ( _i x. _i ) = ( 0 -R 1 ) ) ) |
| 14 |
5 13
|
mpbii |
|- ( T. -> ( _i x. _i ) = ( 0 -R 1 ) ) |
| 15 |
14
|
mptru |
|- ( _i x. _i ) = ( 0 -R 1 ) |