Axiom ax-mulf

Description: Multiplication is an operation on the complex numbers. This deprecated axiom is provided for historical compatibility but is not a bona fide axiom for complex numbers (independent of set theory) since it cannot be interpreted as a first-order or second-order statement (see https://us.metamath.org/downloads/schmidt-cnaxioms.pdf ). It may be deleted in the future and should be avoided for new theorems. Instead, the less specific ax-mulcl should be used. Note that uses of ax-mulf can be eliminated by using the defined operation ( x e. CC , y e. CC |-> ( x x. y ) ) in place of x. , from which this axiom (with the defined operation in place of x. ) follows as a theorem.

This axiom is justified by Theorem axmulf . (New usage is discouraged.) (Contributed by NM, 19-Oct-2004)

	Ref	Expression
Assertion	ax-mulf	$$⊢\times :ℂ\times ℂ⟶ℂ$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cmul	$$class\times$$
1		cc	$$classℂ$$
2	1 1	cxp	$$class\left(ℂ\times ℂ\right)$$
3	2 1 0	wf	$$wff\times :ℂ\times ℂ⟶ℂ$$