Axiom ax-i2m1 11177

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 11153. (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 11111	. . . 4 class i
2		cmul 11114	. . . 4 class ·
3	1, 1, 2	co 7404	. . 3 class (i · i)
4		c1 11110	. . 3 class 1
5		caddc 11112	. . 3 class +
6	3, 4, 5	co 7404	. 2 class ((i · i) + 1)
7		cc0 11109	. 2 class 0
8	6, 7	wceq 1533	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11207  mul02lem2  11392  addrid  11395  cnegex2  11397  ine0  11650  ixi  11844  inelr  12203  c0exALT  41712  sn-1ne2  41718  re1m1e0m0  41830  reixi  41855  sn-inelr  41898