Axiom ax-i2m1 11220

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 11196. (Contributed by NM, 29-Jan-1995.)

Assertion

Ref	Expression
ax-i2m1	⊢ ((i · i) + 1) = 0

Detailed syntax breakdown of Axiom ax-i2m1

Step	Hyp	Ref	Expression
1		ci 11154	. . . 4 class i
2		cmul 11157	. . . 4 class ·
3	1, 1, 2	co 7430	. . 3 class (i · i)
4		c1 11153	. . 3 class 1
5		caddc 11155	. . 3 class +
6	3, 4, 5	co 7430	. 2 class ((i · i) + 1)
7		cc0 11152	. 2 class 0
8	6, 7	wceq 1536	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11250  mul02lem2  11435  addrid  11438  cnegex2  11440  ine0  11695  ixi  11889  inelr  12253  c0exALT  42271  sn-1ne2  42278  re1m1e0m0  42403  reixi  42428  sn-inelr  42473