MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-mulf Unicode version

Axiom ax-mulf 9241
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 . It may be deleted in the future and should be avoided for new theorems. Instead, the less specific ax-mulcl 9223 should be used. Note that uses of ax-mulf 9241 can be eliminated by using the defined operation in place of , from which this axiom (with the defined operation in place of ) follows as a theorem.

This axiom is justified by theorem axmulf 9192. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Ref Expression

Detailed syntax breakdown of Axiom ax-mulf
StepHypRef Expression
1 cc 9159 . . 3
21, 1cxp 4860 . 2
3 cmul 9166 . 2
42, 1, 3wf 5434 1
Colors of variables: wff set class
This axiom is referenced by:  mulnzcnopr  9855  mulex  10854  rlimmul  12969  mulcn  19912  iimulcn  19978  dvdsmulf1o  22000  fsumdvdsmul  22001  efghgrp  22982  cnrngo  23012  cncvc  23083  rmulccn  25537  xrge0pluscn  25549
  Copyright terms: Public domain W3C validator