Axiom ax-i2m1 7930

Description: i-squared equals -1 (expressed as i-squared plus 1 is 0). Axiom for real and complex numbers, justified by Theorem axi2m1 7888. (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 7827	. . . 4 class i
2		cmul 7830	. . . 4 class ·
3	1, 1, 2	co 5888	. . 3 class (i · i)
4		c1 7826	. . 3 class 1
5		caddc 7828	. . 3 class +
6	3, 4, 5	co 5888	. 2 class ((i · i) + 1)
7		cc0 7825	. 2 class 0
8	6, 7	wceq 1363	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  7963  ine0  8365  ixi  8554  inelr  8555