Axiom ax-i2m1 8284

Description: i-squared equals -1 (expressed as i-squared plus 1 is 0). Axiom for real and complex numbers, justified by Theorem axi2m1 8242. (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 8181	. . . 4 class i
2		cmul 8184	. . . 4 class ·
3	1, 1, 2	co 6085	. . 3 class (i · i)
4		c1 8180	. . 3 class 1
5		caddc 8182	. . 3 class +
6	3, 4, 5	co 6085	. 2 class ((i · i) + 1)
7		cc0 8179	. 2 class 0
8	6, 7	wceq 1402	1 wff ((i · i) + 1) = 0

This axiom is used by:  0cn  8318  ine0  8721  ixi  8912  inelr  8913