Metamath Proof Explorer
Description: Move the left term in a sum on the RHS to the LHS. (Contributed by David
A. Wheeler, 11-Oct-2018)
|
|
Ref |
Expression |
|
Hypotheses |
mvrladdi.1 |
⊢ 𝐵 ∈ ℂ |
|
|
mvrladdi.2 |
⊢ 𝐶 ∈ ℂ |
|
|
mvrladdi.3 |
⊢ 𝐴 = ( 𝐵 + 𝐶 ) |
|
Assertion |
mvrladdi |
⊢ ( 𝐴 − 𝐵 ) = 𝐶 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
mvrladdi.1 |
⊢ 𝐵 ∈ ℂ |
2 |
|
mvrladdi.2 |
⊢ 𝐶 ∈ ℂ |
3 |
|
mvrladdi.3 |
⊢ 𝐴 = ( 𝐵 + 𝐶 ) |
4 |
1 2 3
|
comraddi |
⊢ 𝐴 = ( 𝐶 + 𝐵 ) |
5 |
4
|
oveq1i |
⊢ ( 𝐴 − 𝐵 ) = ( ( 𝐶 + 𝐵 ) − 𝐵 ) |
6 |
2 1
|
pncan3oi |
⊢ ( ( 𝐶 + 𝐵 ) − 𝐵 ) = 𝐶 |
7 |
5 6
|
eqtri |
⊢ ( 𝐴 − 𝐵 ) = 𝐶 |