Axiom ax-i2m1 10004

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 9980. (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 9938	. . . 4 class i
2		cmul 9941	. . . 4 class ·
3	1, 1, 2	co 6650	. . 3 class (i · i)
4		c1 9937	. . 3 class 1
5		caddc 9939	. . 3 class +
6	3, 4, 5	co 6650	. 2 class ((i · i) + 1)
7		cc0 9936	. 2 class 0
8	6, 7	wceq 1483	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  10032  mul02lem2  10213  addid1  10216  cnegex2  10218  ine0  10465  ixi  10656  inelr  11010