Axiom ax-mulf 7743

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 7718 should be used. Note that uses of ax-mulf 7743 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 7677. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Assertion

Ref	Expression
ax-mulf	|- x. : ( CC X. CC ) --> CC

Detailed syntax breakdown of Axiom ax-mulf

Step	Hyp	Ref	Expression
1		cc 7618	. . 3 class CC
2	1, 1	cxp 4537	. 2 class ( CC X. CC )
3		cmul 7625	. 2 class x.
4	2, 1, 3	wf 5119	1 wff x. : ( CC X. CC ) --> CC

This axiom is referenced by:  mulcncntop  12723