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

Axiom ax-mulf 9121
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 9103 should be used. Note that uses of ax-mulf 9121 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 9072. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Ref Expression

Detailed syntax breakdown of Axiom ax-mulf
StepHypRef Expression
1 cc 9039 . . 3
21, 1cxp 4917 . 2
3 cmul 9046 . 2
42, 1, 3wf 5497 1
Colors of variables: wff set class
This axiom is referenced by:  mulnzcnopr  9719  mulex  10662  rlimmul  12489  mulcn  18948  iimulcn  19014  dvdsmulf1o  21030  fsumdvdsmul  21031  efghgrp  22012  cnrngo  22042  cncvc  22113  rmulccn  24363  xrge0pluscn  24375
  Copyright terms: Public domain W3C validator