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Metamath Proof Explorer

Theorem mvrraddi

Description: Move the right term in a sum on the RHS to the LHS. (Contributed by David A. Wheeler, 11-Oct-2018)

Ref Expression
Hypotheses mvrraddi.1 ⊢ 𝐵 ∈ ℂ
mvrraddi.2 ⊢ 𝐶 ∈ ℂ
mvrraddi.3 ⊢ 𝐴 = ( 𝐵 + 𝐶 )
Assertion mvrraddi ( 𝐴 − 𝐶 ) = 𝐵

Proof

Step Hyp Ref Expression
1 mvrraddi.1 ⊢ 𝐵 ∈ ℂ
2 mvrraddi.2 ⊢ 𝐶 ∈ ℂ
3 mvrraddi.3 ⊢ 𝐴 = ( 𝐵 + 𝐶 )
4 3 oveq1i ⊢ ( 𝐴 − 𝐶 ) = ( ( 𝐵 + 𝐶 ) − 𝐶 )
5 1 2 pncan3oi ⊢ ( ( 𝐵 + 𝐶 ) − 𝐶 ) = 𝐵
6 4 5 eqtri ⊢ ( 𝐴 − 𝐶 ) = 𝐵