Axiom ax-i2m1 10458

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 10434. (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 10392	. . . 4 class i
2		cmul 10395	. . . 4 class ·
3	1, 1, 2	co 7023	. . 3 class (i · i)
4		c1 10391	. . 3 class 1
5		caddc 10393	. . 3 class +
6	3, 4, 5	co 7023	. 2 class ((i · i) + 1)
7		cc0 10390	. 2 class 0
8	6, 7	wceq 1525	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  10486  mul02lem2  10670  addid1  10673  cnegex2  10675  ine0  10929  ixi  11123  inelr  11482  c0exALT  38700