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- 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	⊢ · : ( ℂ × ℂ ) ⟶ ℂ

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cmul	⊢ ·
1		cc	⊢ ℂ
2	1 1	cxp	⊢ ( ℂ × ℂ )
3	2 1 0	wf	⊢ · : ( ℂ × ℂ ) ⟶ ℂ