Description: Move LHS right addition to RHS. (Contributed by David A. Wheeler, 15-Oct-2018)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mvlraddd.1 | |- ( ph -> A e. CC ) |
|
mvlraddd.2 | |- ( ph -> B e. CC ) |
||
mvlraddd.3 | |- ( ph -> ( A + B ) = C ) |
||
Assertion | mvlraddd | |- ( ph -> A = ( C - B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mvlraddd.1 | |- ( ph -> A e. CC ) |
|
2 | mvlraddd.2 | |- ( ph -> B e. CC ) |
|
3 | mvlraddd.3 | |- ( ph -> ( A + B ) = C ) |
|
4 | 1 2 | pncand | |- ( ph -> ( ( A + B ) - B ) = A ) |
5 | 3 | oveq1d | |- ( ph -> ( ( A + B ) - B ) = ( C - B ) ) |
6 | 4 5 | eqtr3d | |- ( ph -> A = ( C - B ) ) |