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Metamath Proof Explorer

Theorem comraddi

Description: Commute RHS addition. See addcomli to commute addition on LHS. (Contributed by David A. Wheeler, 11-Oct-2018)

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

Proof

Step Hyp Ref Expression
1 comraddi.1 ⊢ 𝐵 ∈ ℂ
2 comraddi.2 ⊢ 𝐶 ∈ ℂ
3 comraddi.3 ⊢ 𝐴 = ( 𝐵 + 𝐶 )
4 1 2 addcomi ⊢ ( 𝐵 + 𝐶 ) = ( 𝐶 + 𝐵 )
5 3 4 eqtri ⊢ 𝐴 = ( 𝐶 + 𝐵 )