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Axiom ax-addcom 6982
Description: Addition commutes. Axiom for real and complex numbers, justified by theorem axaddcom 6942. Proofs should normally use addcom 7148 instead. (New usage is discouraged.) (Contributed by Jim Kingdon, 17-Jan-2020.)
Assertion
Ref Expression
ax-addcom ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))

Detailed syntax breakdown of Axiom ax-addcom
StepHypRef Expression
1 cA . . . 4 class 𝐴
2 cc 6885 . . . 4 class
31, 2wcel 1393 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1393 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 97 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 caddc 6890 . . . 4 class +
81, 4, 7co 5512 . . 3 class (𝐴 + 𝐵)
94, 1, 7co 5512 . . 3 class (𝐵 + 𝐴)
108, 9wceq 1243 . 2 wff (𝐴 + 𝐵) = (𝐵 + 𝐴)
116, 10wi 4 1 wff ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))
Colors of variables: wff set class
This axiom is referenced by:  addcom  7148
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