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| Mirrors > Home > MPE Home > Th. List > ax-i2m1 | Structured version Visualization version GIF version | ||
| 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 11199. (Contributed by NM, 29-Jan-1995.) |
| Ref | Expression |
|---|---|
| ax-i2m1 | ⊢ ((i · i) + 1) = 0 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ci 11157 | . . . 4 class i | |
| 2 | cmul 11160 | . . . 4 class · | |
| 3 | 1, 1, 2 | co 7431 | . . 3 class (i · i) |
| 4 | c1 11156 | . . 3 class 1 | |
| 5 | caddc 11158 | . . 3 class + | |
| 6 | 3, 4, 5 | co 7431 | . 2 class ((i · i) + 1) |
| 7 | cc0 11155 | . 2 class 0 | |
| 8 | 6, 7 | wceq 1540 | 1 wff ((i · i) + 1) = 0 |
| Colors of variables: wff setvar class |
| This axiom is referenced by: 0cn 11253 mul02lem2 11438 addrid 11441 cnegex2 11443 ine0 11698 ixi 11892 inelr 12256 c0exALT 42293 sn-1ne2 42300 re1m1e0m0 42427 reixi 42452 sn-inelr 42497 |
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