Axiom ax-i2m1 7854

Description: i-squared equals -1 (expressed as i-squared plus 1 is 0). Axiom for real and complex numbers, justified by Theorem axi2m1 7812. (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 7751	. . . 4 class i
2		cmul 7754	. . . 4 class ·
3	1, 1, 2	co 5841	. . 3 class (i · i)
4		c1 7750	. . 3 class 1
5		caddc 7752	. . 3 class +
6	3, 4, 5	co 5841	. 2 class ((i · i) + 1)
7		cc0 7749	. 2 class 0
8	6, 7	wceq 1343	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  7887  ine0  8288  ixi  8477  inelr  8478