Axiom ax-i2m1 11104

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 11080. (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 11038	. . . 4 class i
2		cmul 11041	. . . 4 class ·
3	1, 1, 2	co 7363	. . 3 class (i · i)
4		c1 11037	. . 3 class 1
5		caddc 11039	. . 3 class +
6	3, 4, 5	co 7363	. 2 class ((i · i) + 1)
7		cc0 11036	. 2 class 0
8	6, 7	wceq 1547	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11134  mul02lem2  11321  addrid  11324  cnegex2  11326  ine0  11583  ixi  11777  c0exALT  42737  sn-1ne2  42749  re1m1e0m0  42875  reixi  42901  sn-inelr  42978