Axiom ax-i2m1 11156

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 11132. (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 11090	. . . 4 class i
2		cmul 11093	. . . 4 class ·
3	1, 1, 2	co 7400	. . 3 class (i · i)
4		c1 11089	. . 3 class 1
5		caddc 11091	. . 3 class +
6	3, 4, 5	co 7400	. 2 class ((i · i) + 1)
7		cc0 11088	. 2 class 0
8	6, 7	wceq 1563	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11186  mul02lem2  11375  addrid  11378  cnegex2  11380  ine0  11637  ixi  11831  c0exALT  42880  sn-1ne2  42892  re1m1e0m0  43018  reixi  43044  sn-inelr  43121