Description: The number 10 is real. (Contributed by NM, 5-Feb-2007) (Revised by AV, 8-Sep-2021) Reduce dependencies on axioms. (Revised by Steven Nguyen, 8-Oct-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 10re | ⊢ ; 1 0 ∈ ℝ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-dec | ⊢ ; 1 0 = ( ( ( 9 + 1 ) · 1 ) + 0 ) | |
| 2 | 9re | ⊢ 9 ∈ ℝ | |
| 3 | 1re | ⊢ 1 ∈ ℝ | |
| 4 | 2 3 | readdcli | ⊢ ( 9 + 1 ) ∈ ℝ |
| 5 | 4 3 | remulcli | ⊢ ( ( 9 + 1 ) · 1 ) ∈ ℝ |
| 6 | 0re | ⊢ 0 ∈ ℝ | |
| 7 | 5 6 | readdcli | ⊢ ( ( ( 9 + 1 ) · 1 ) + 0 ) ∈ ℝ |
| 8 | 1 7 | eqeltri | ⊢ ; 1 0 ∈ ℝ |