Metamath Proof Explorer


Theorem mvrladdi

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 ( 𝐴𝐵 ) = 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 ( 𝐴𝐵 ) = ( ( 𝐶 + 𝐵 ) − 𝐵 )
6 2 1 pncan3oi ( ( 𝐶 + 𝐵 ) − 𝐵 ) = 𝐶
7 5 6 eqtri ( 𝐴𝐵 ) = 𝐶