MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-i2m1 Unicode version

Axiom ax-i2m1 8805
Description: i-squared equals -1 (expressed as i-squared plus 1 is 0). Axiom 12 of 22 for real and complex numbers, justified by theorem axi2m1 8781. (Contributed by NM, 29-Jan-1995.)
Assertion
Ref Expression
ax-i2m1  |-  ( ( _i  x.  _i )  +  1 )  =  0

Detailed syntax breakdown of Axiom ax-i2m1
StepHypRef Expression
1 ci 8739 . . . 4  class  _i
2 cmul 8742 . . . 4  class  x.
31, 1, 2co 5858 . . 3  class  ( _i  x.  _i )
4 c1 8738 . . 3  class  1
5 caddc 8740 . . 3  class  +
63, 4, 5co 5858 . 2  class  ( ( _i  x.  _i )  +  1 )
7 cc0 8737 . 2  class  0
86, 7wceq 1623 1  wff  ( ( _i  x.  _i )  +  1 )  =  0
Colors of variables: wff set class
This axiom is referenced by:  0cn  8831  mul02lem2  8989  addid1  8992  cnegex2  8994  ine0  9215  ixi  9397  inelr  9736  cnegvex2  25660
  Copyright terms: Public domain W3C validator