Description: The ordering relation of the field of reals. (Contributed by Thierry Arnoux, 21-Jan-2018)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | rele2 | ⊢ ≤ = ( le ‘ ℝfld ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | reex | ⊢ ℝ ∈ V | |
| 2 | df-refld | ⊢ ℝfld = ( ℂfld ↾s ℝ ) | |
| 3 | cnfldle | ⊢ ≤ = ( le ‘ ℂfld ) | |
| 4 | 2 3 | ressle | ⊢ ( ℝ ∈ V → ≤ = ( le ‘ ℝfld ) ) |
| 5 | 1 4 | ax-mp | ⊢ ≤ = ( le ‘ ℝfld ) |