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

Axiom ax-i2m1 10598
 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 10574. (Contributed by NM, 29-Jan-1995.)
Assertion
Ref Expression
ax-i2m1 ((i · i) + 1) = 0

Detailed syntax breakdown of Axiom ax-i2m1
StepHypRef Expression
1 ci 10532 . . . 4 class i
2 cmul 10535 . . . 4 class ·
31, 1, 2co 7139 . . 3 class (i · i)
4 c1 10531 . . 3 class 1
5 caddc 10533 . . 3 class +
63, 4, 5co 7139 . 2 class ((i · i) + 1)
7 cc0 10530 . 2 class 0
86, 7wceq 1538 1 wff ((i · i) + 1) = 0
 Colors of variables: wff setvar class This axiom is referenced by:  0cn  10626  mul02lem2  10810  addid1  10813  cnegex2  10815  ine0  11068  ixi  11262  inelr  11619  c0exALT  39457  sn-1ne2  39463  re1m1e0m0  39532  reixi  39556  sn-inelr  39587
 Copyright terms: Public domain W3C validator