Mathbox for Glauco Siliprandi |
< Previous
Next >
Nearby theorems |
||
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 12400 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ) | |
2 | 1 | ssriv 3971 | 1 ⊢ ℝ+ ⊆ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3936 ℂcc 10535 ℝ+crp 12390 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 ax-resscn 10594 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-in 3943 df-ss 3952 df-rp 12391 |
This theorem is referenced by: stirlinglem8 42386 |
Copyright terms: Public domain | W3C validator |