Axiom ax-i2m1 11295

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 11271. (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 11229	. . . 4 class i
2		cmul 11232	. . . 4 class ·
3	1, 1, 2	co 7443	. . 3 class (i · i)
4		c1 11228	. . 3 class 1
5		caddc 11230	. . 3 class +
6	3, 4, 5	co 7443	. 2 class ((i · i) + 1)
7		cc0 11227	. 2 class 0
8	6, 7	wceq 1570	1 wff ((i · i) + 1) = 0

This axiom is used by:  0cn  11325  mul02lem2  11514  addrid  11517  cnegex2  11519  ine0  11778  ixi  11972  c0exALT  43496  sn-1ne2  43523  re1m1e0m0  43641  reixi  43667  sn-inelr  43744