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Axiom ax-addcl 6779
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 6750. Proofs should normally use addcl 6804 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 6709 . . . 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 6714 . . . 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  6804
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