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Axiom ax-addcl 6739
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 6710. Proofs should normally use addcl 6764 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl ((A B ℂ) → (A + B) ℂ)

Detailed syntax breakdown of Axiom ax-addcl
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
63, 5wa 97 . 2 wff (A B ℂ)
7 caddc 6674 . . . 4 class +
81, 4, 7co 5455 . . 3 class (A + B)
98, 2wcel 1390 . 2 wff (A + B)
106, 9wi 4 1 wff ((A B ℂ) → (A + B) ℂ)
Colors of variables: wff set class
This axiom is referenced by:  addcl  6764
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