Axiom ax-i2m1 11186

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 11162. (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 11120	. . . 4 class i
2		cmul 11123	. . . 4 class ·
3	1, 1, 2	co 7423	. . 3 class (i · i)
4		c1 11119	. . 3 class 1
5		caddc 11121	. . 3 class +
6	3, 4, 5	co 7423	. 2 class ((i · i) + 1)
7		cc0 11118	. 2 class 0
8	6, 7	wceq 1570	1 wff ((i · i) + 1) = 0

This axiom is used by:  0cn  11216  mul02lem2  11405  addrid  11408  cnegex2  11410  ine0  11667  ixi  11861  c0exALT  43053  sn-1ne2  43065  re1m1e0m0  43191  reixi  43217  sn-inelr  43294