Axiom ax-i2m1 10870

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 10846. (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 10804	. . . 4 class i
2		cmul 10807	. . . 4 class ·
3	1, 1, 2	co 7255	. . 3 class (i · i)
4		c1 10803	. . 3 class 1
5		caddc 10805	. . 3 class +
6	3, 4, 5	co 7255	. 2 class ((i · i) + 1)
7		cc0 10802	. 2 class 0
8	6, 7	wceq 1539	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  10898  mul02lem2  11082  addid1  11085  cnegex2  11087  ine0  11340  ixi  11534  inelr  11893  c0exALT  40210  sn-1ne2  40216  re1m1e0m0  40301  reixi  40325  sn-inelr  40356