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Axiom ax-mulf 9071
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 http://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 9053 should be used. Note that uses of ax-mulf 9071 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 9022. (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
StepHypRef Expression
1 cc 8989 . . 3  class  CC
21, 1cxp 4877 . 2  class  ( CC 
X.  CC )
3 cmul 8996 . 2  class  x.
42, 1, 3wf 5451 1  wff  x.  :
( CC  X.  CC )
--> CC
Colors of variables: wff set class
This axiom is referenced by:  mulnzcnopr  9669  mulex  10612  rlimmul  12439  mulcn  18898  iimulcn  18964  dvdsmulf1o  20980  fsumdvdsmul  20981  efghgrp  21962  cnrngo  21992  cncvc  22063  rmulccn  24315  xrge0pluscn  24327
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