Description: Swap the first two variables in an equation with addition on the right, converting it into a subtraction. Version of mvrraddd with a commuted consequent, and of mvlraddd with a commuted hypothesis.
EDITORIAL: The label for this theorem is questionable. Do not move until it would have 7 uses: current additional uses: (none). (Contributed by SN, 21-Aug-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | raddswap12d.b | |- ( ph -> B e. CC ) |
|
| raddswap12d.c | |- ( ph -> C e. CC ) |
||
| raddswap12d.1 | |- ( ph -> A = ( B + C ) ) |
||
| Assertion | raddswap12d | |- ( ph -> B = ( A - C ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | raddswap12d.b | |- ( ph -> B e. CC ) |
|
| 2 | raddswap12d.c | |- ( ph -> C e. CC ) |
|
| 3 | raddswap12d.1 | |- ( ph -> A = ( B + C ) ) |
|
| 4 | 1 2 3 | mvrraddd | |- ( ph -> ( A - C ) = B ) |
| 5 | 4 | eqcomd | |- ( ph -> B = ( A - C ) ) |