Step |
Hyp |
Ref |
Expression |
1 |
|
add4 |
|- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A + B ) + ( C + D ) ) = ( ( A + C ) + ( B + D ) ) ) |
2 |
|
addcom |
|- ( ( B e. CC /\ D e. CC ) -> ( B + D ) = ( D + B ) ) |
3 |
2
|
ad2ant2l |
|- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( B + D ) = ( D + B ) ) |
4 |
3
|
oveq2d |
|- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A + C ) + ( B + D ) ) = ( ( A + C ) + ( D + B ) ) ) |
5 |
1 4
|
eqtrd |
|- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A + B ) + ( C + D ) ) = ( ( A + C ) + ( D + B ) ) ) |