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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 10003 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 9954 | . 2 class ≤ | |
2 | cxr 9952 | . . . 4 class ℝ* | |
3 | 2, 2 | cxp 5036 | . . 3 class (ℝ* × ℝ*) |
4 | clt 9953 | . . . 4 class < | |
5 | 4 | ccnv 5037 | . . 3 class ◡ < |
6 | 3, 5 | cdif 3537 | . 2 class ((ℝ* × ℝ*) ∖ ◡ < ) |
7 | 1, 6 | wceq 1475 | 1 wff ≤ = ((ℝ* × ℝ*) ∖ ◡ < ) |
Colors of variables: wff setvar class |
This definition is referenced by: lerelxr 9980 xrlenlt 9982 leiso 13100 gtiso 28861 |
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