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 e. RR |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-dec | |- ; 1 0 = ( ( ( 9 + 1 ) x. 1 ) + 0 ) |
|
| 2 | 9re | |- 9 e. RR |
|
| 3 | 1re | |- 1 e. RR |
|
| 4 | 2 3 | readdcli | |- ( 9 + 1 ) e. RR |
| 5 | 4 3 | remulcli | |- ( ( 9 + 1 ) x. 1 ) e. RR |
| 6 | 0re | |- 0 e. RR |
|
| 7 | 5 6 | readdcli | |- ( ( ( 9 + 1 ) x. 1 ) + 0 ) e. RR |
| 8 | 1 7 | eqeltri | |- ; 1 0 e. RR |