Axiom ax-i2m1 11252

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 11228. (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 11186	. . . 4 class i
2		cmul 11189	. . . 4 class ·
3	1, 1, 2	co 7448	. . 3 class (i · i)
4		c1 11185	. . 3 class 1
5		caddc 11187	. . 3 class +
6	3, 4, 5	co 7448	. 2 class ((i · i) + 1)
7		cc0 11184	. 2 class 0
8	6, 7	wceq 1537	1 wff ((i · i) + 1) = 0

This axiom is referenced by:  0cn  11282  mul02lem2  11467  addrid  11470  cnegex2  11472  ine0  11725  ixi  11919  inelr  12283  c0exALT  42247  sn-1ne2  42254  re1m1e0m0  42373  reixi  42398  sn-inelr  42443