Step |
Hyp |
Ref |
Expression |
1 |
|
df-neg |
|- -u B = ( 0 - B ) |
2 |
1
|
oveq2i |
|- ( A - -u B ) = ( A - ( 0 - B ) ) |
3 |
|
0cn |
|- 0 e. CC |
4 |
|
subsub |
|- ( ( A e. CC /\ 0 e. CC /\ B e. CC ) -> ( A - ( 0 - B ) ) = ( ( A - 0 ) + B ) ) |
5 |
3 4
|
mp3an2 |
|- ( ( A e. CC /\ B e. CC ) -> ( A - ( 0 - B ) ) = ( ( A - 0 ) + B ) ) |
6 |
2 5
|
eqtrid |
|- ( ( A e. CC /\ B e. CC ) -> ( A - -u B ) = ( ( A - 0 ) + B ) ) |
7 |
|
subid1 |
|- ( A e. CC -> ( A - 0 ) = A ) |
8 |
7
|
adantr |
|- ( ( A e. CC /\ B e. CC ) -> ( A - 0 ) = A ) |
9 |
8
|
oveq1d |
|- ( ( A e. CC /\ B e. CC ) -> ( ( A - 0 ) + B ) = ( A + B ) ) |
10 |
6 9
|
eqtrd |
|- ( ( A e. CC /\ B e. CC ) -> ( A - -u B ) = ( A + B ) ) |