Theorem axaddcl

Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, derived from ZF set theory. This construction-dependent theorem should not be referenced directly, nor should the proven axiom ax-addcl be used later. Instead, in most cases use addcl . (Contributed by NM, 14-Jun-1995) (New usage is discouraged.)

	Ref	Expression
Assertion	axaddcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A+B\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		axaddf	$$⊢+:ℂ\times ℂ⟶ℂ$$
2	1	fovcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A+B\in ℂ$$