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Mirrors > Home > MPE Home > Th. List > Mathboxes > rr2sscn2 | Structured version Visualization version GIF version |
Description: The cartesian square of ℝ is a subset of the cartesian square of ℂ. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
Ref | Expression |
---|---|
rr2sscn2 | ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-resscn 10582 | . 2 ⊢ ℝ ⊆ ℂ | |
2 | xpss12 5563 | . 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ)) | |
3 | 1, 1, 2 | mp2an 688 | 1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ) |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3933 × cxp 5546 ℂcc 10523 ℝcr 10524 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-resscn 10582 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-in 3940 df-ss 3949 df-opab 5120 df-xp 5554 |
This theorem is referenced by: ovolval2lem 42802 ovolval2 42803 ovolval3 42806 |
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