| Mathbox for Steven Nguyen |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > rpsscn | Structured version Visualization version GIF version | ||
| Description: The positive reals are a subset of the complex numbers. (Contributed by SN, 1-Oct-2025.) |
| Ref | Expression |
|---|---|
| rpsscn | ⊢ ℝ+ ⊆ ℂ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rpssre 13042 | . 2 ⊢ ℝ+ ⊆ ℝ | |
| 2 | ax-resscn 11212 | . 2 ⊢ ℝ ⊆ ℂ | |
| 3 | 1, 2 | sstri 3993 | 1 ⊢ ℝ+ ⊆ ℂ |
| Colors of variables: wff setvar class |
| Syntax hints: ⊆ wss 3951 ℂcc 11153 ℝcr 11154 ℝ+crp 13034 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-resscn 11212 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-ss 3968 df-rp 13035 |
| This theorem is referenced by: readvrec2 42391 |
| Copyright terms: Public domain | W3C validator |