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Mathbox for Glauco Siliprandi |
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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 12987 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ) | |
2 | 1 | ssriv 3981 | 1 ⊢ ℝ+ ⊆ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3943 ℂcc 11107 ℝ+crp 12977 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 ax-resscn 11166 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-rab 3427 df-v 3470 df-in 3950 df-ss 3960 df-rp 12978 |
This theorem is referenced by: stirlinglem8 45350 |
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