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Metamath Proof Explorer

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	\|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		axaddf	\|- + : ( CC X. CC ) --> CC
2	1	fovcl	\|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )