Axiom ax-i2m1 11223

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 11199. (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 11157	. . . 4 class i
2		cmul 11160	. . . 4 class ·
3	1, 1, 2	co 7431	. . 3 class (i · i)
4		c1 11156	. . 3 class 1
5		caddc 11158	. . 3 class +
6	3, 4, 5	co 7431	. 2 class ((i · i) + 1)
7		cc0 11155	. 2 class 0
8	6, 7	wceq 1540	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11253  mul02lem2  11438  addrid  11441  cnegex2  11443  ine0  11698  ixi  11892  inelr  12256  c0exALT  42293  sn-1ne2  42300  re1m1e0m0  42427  reixi  42452  sn-inelr  42497