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Axiom ax-addass 6745
Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 6716. Proofs should normally use addass 6769 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addass ((A B 𝐶 ℂ) → ((A + B) + 𝐶) = (A + (B + 𝐶)))

Detailed syntax breakdown of Axiom ax-addass
StepHypRef Expression
1 cA . . . 4 class A
2 cc 6669 . . . 4 class
31, 2wcel 1390 . . 3 wff A
4 cB . . . 4 class B
54, 2wcel 1390 . . 3 wff B
6 cC . . . 4 class 𝐶
76, 2wcel 1390 . . 3 wff 𝐶
83, 5, 7w3a 884 . 2 wff (A B 𝐶 ℂ)
9 caddc 6674 . . . . 5 class +
101, 4, 9co 5455 . . . 4 class (A + B)
1110, 6, 9co 5455 . . 3 class ((A + B) + 𝐶)
124, 6, 9co 5455 . . . 4 class (B + 𝐶)
131, 12, 9co 5455 . . 3 class (A + (B + 𝐶))
1411, 13wceq 1242 . 2 wff ((A + B) + 𝐶) = (A + (B + 𝐶))
158, 14wi 4 1 wff ((A B 𝐶 ℂ) → ((A + B) + 𝐶) = (A + (B + 𝐶)))
Colors of variables: wff set class
This axiom is referenced by:  addass  6769
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