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Axiom ax-addcom 6763
Description: Addition commutes. Axiom for real and complex numbers, justified by theorem axaddcom 6734. Proofs should normally use addcom 6927 instead. (New usage is discouraged.) (Contributed by Jim Kingdon, 17-Jan-2020.)
Assertion
Ref Expression
ax-addcom ((A B ℂ) → (A + B) = (B + A))

Detailed syntax breakdown of Axiom ax-addcom
StepHypRef Expression
1 cA . . . 4 class A
2 cc 6689 . . . 4 class
31, 2wcel 1390 . . 3 wff A
4 cB . . . 4 class B
54, 2wcel 1390 . . 3 wff B
63, 5wa 97 . 2 wff (A B ℂ)
7 caddc 6694 . . . 4 class +
81, 4, 7co 5455 . . 3 class (A + B)
94, 1, 7co 5455 . . 3 class (B + A)
108, 9wceq 1242 . 2 wff (A + B) = (B + A)
116, 10wi 4 1 wff ((A B ℂ) → (A + B) = (B + A))
Colors of variables: wff set class
This axiom is referenced by:  addcom  6927
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