Step |
Hyp |
Ref |
Expression |
1 |
|
readdcl |
|- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR ) |
2 |
|
resubsub4 |
|- ( ( ( A + B ) e. RR /\ A e. RR /\ C e. RR ) -> ( ( ( A + B ) -R A ) -R C ) = ( ( A + B ) -R ( A + C ) ) ) |
3 |
1 2
|
stoic4a |
|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( ( A + B ) -R A ) -R C ) = ( ( A + B ) -R ( A + C ) ) ) |
4 |
|
repncan2 |
|- ( ( A e. RR /\ B e. RR ) -> ( ( A + B ) -R A ) = B ) |
5 |
4
|
3adant3 |
|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A + B ) -R A ) = B ) |
6 |
5
|
oveq1d |
|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( ( A + B ) -R A ) -R C ) = ( B -R C ) ) |
7 |
3 6
|
eqtr3d |
|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A + B ) -R ( A + C ) ) = ( B -R C ) ) |