Description: Cancellation law for subtraction. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidd.1 | |- ( ph -> A e. CC ) |
|
pncand.2 | |- ( ph -> B e. CC ) |
||
subaddd.3 | |- ( ph -> C e. CC ) |
||
Assertion | nppcan3d | |- ( ph -> ( ( A - B ) + ( C + B ) ) = ( A + C ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | |- ( ph -> A e. CC ) |
|
2 | pncand.2 | |- ( ph -> B e. CC ) |
|
3 | subaddd.3 | |- ( ph -> C e. CC ) |
|
4 | nppcan3 | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A - B ) + ( C + B ) ) = ( A + C ) ) |
|
5 | 1 2 3 4 | syl3anc | |- ( ph -> ( ( A - B ) + ( C + B ) ) = ( A + C ) ) |