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| Mirrors > Home > MPE Home > Th. List > df-le | Structured version Visualization version GIF version | ||
| Description: Define 'less than or equal to' on the extended real subset of complex numbers. Theorem leloe 11347 relates it to 'less than' for reals. (Contributed by NM, 13-Oct-2005.) |
| Ref | Expression |
|---|---|
| df-le | ⊢ ≤ = ((ℝ* × ℝ*) ∖ ◡ < ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cle 11296 | . 2 class ≤ | |
| 2 | cxr 11294 | . . . 4 class ℝ* | |
| 3 | 2, 2 | cxp 5683 | . . 3 class (ℝ* × ℝ*) |
| 4 | clt 11295 | . . . 4 class < | |
| 5 | 4 | ccnv 5684 | . . 3 class ◡ < |
| 6 | 3, 5 | cdif 3948 | . 2 class ((ℝ* × ℝ*) ∖ ◡ < ) |
| 7 | 1, 6 | wceq 1540 | 1 wff ≤ = ((ℝ* × ℝ*) ∖ ◡ < ) |
| Colors of variables: wff setvar class |
| This definition is referenced by: lerelxr 11324 xrlenlt 11326 leiso 14498 gtiso 32710 |
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