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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rpssxr | Structured version Visualization version GIF version |
Description: The positive reals are a subset of the extended reals. (Contributed by Glauco Siliprandi, 5-Feb-2022.) |
Ref | Expression |
---|---|
rpssxr | ⊢ ℝ+ ⊆ ℝ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpssre 12923 | . 2 ⊢ ℝ+ ⊆ ℝ | |
2 | ressxr 11200 | . 2 ⊢ ℝ ⊆ ℝ* | |
3 | 1, 2 | sstri 3954 | 1 ⊢ ℝ+ ⊆ ℝ* |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3911 ℝcr 11051 ℝ*cxr 11189 ℝ+crp 12916 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-rab 3409 df-v 3448 df-un 3916 df-in 3918 df-ss 3928 df-xr 11194 df-rp 12917 |
This theorem is referenced by: cnrefiisplem 44077 |
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