Axiom ax-i2m1 10948

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 10924. (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 10882	. . . 4 class i
2		cmul 10885	. . . 4 class ·
3	1, 1, 2	co 7284	. . 3 class (i · i)
4		c1 10881	. . 3 class 1
5		caddc 10883	. . 3 class +
6	3, 4, 5	co 7284	. 2 class ((i · i) + 1)
7		cc0 10880	. 2 class 0
8	6, 7	wceq 1539	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  10976  mul02lem2  11161  addid1  11164  cnegex2  11166  ine0  11419  ixi  11613  inelr  11972  c0exALT  40296  sn-1ne2  40302  re1m1e0m0  40387  reixi  40411  sn-inelr  40442