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| Mirrors > Home > MPE Home > Th. List > Mathboxes > rrpsscn | Structured version Visualization version GIF version | ||
| Description: The positive reals are a subset of the complex numbers. (Contributed by Glauco Siliprandi, 29-Jun-2017.) | 
| Ref | Expression | 
|---|---|
| rrpsscn | ⊢ ℝ+ ⊆ ℂ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | rpcn 13046 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ) | |
| 2 | 1 | ssriv 3986 | 1 ⊢ ℝ+ ⊆ ℂ | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊆ wss 3950 ℂcc 11154 ℝ+crp 13035 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-resscn 11213 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-rab 3436 df-ss 3967 df-rp 13036 | 
| This theorem is referenced by: stirlinglem8 46101 | 
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