ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-i2m1 Structured version   GIF version

Axiom ax-i2m1 6748
Description: i-squared equals -1 (expressed as i-squared plus 1 is 0). Axiom for real and complex numbers, justified by theorem axi2m1 6719. (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 6673 . . . 4 class i
2 cmul 6676 . . . 4 class ·
31, 1, 2co 5455 . . 3 class (i · i)
4 c1 6672 . . 3 class 1
5 caddc 6674 . . 3 class +
63, 4, 5co 5455 . 2 class ((i · i) + 1)
7 cc0 6671 . 2 class 0
86, 7wceq 1242 1 wff ((i · i) + 1) = 0
Colors of variables: wff set class
This axiom is referenced by:  0cn  6777  ine0  7147  ixi  7327  inelr  7328
  Copyright terms: Public domain W3C validator