Axiom ax-i2m1 11196

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 11172. (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 11130	. . . 4 class i
2		cmul 11133	. . . 4 class ·
3	1, 1, 2	co 7417	. . 3 class (i · i)
4		c1 11129	. . 3 class 1
5		caddc 11131	. . 3 class +
6	3, 4, 5	co 7417	. 2 class ((i · i) + 1)
7		cc0 11128	. 2 class 0
8	6, 7	wceq 1570	1 wff ((i · i) + 1) = 0

This axiom is used by:  0cn  11226  mul02lem2  11415  addrid  11418  cnegex2  11420  ine0  11677  ixi  11871  c0exALT  43127  sn-1ne2  43154  re1m1e0m0  43280  reixi  43306  sn-inelr  43383