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Mathbox for Glauco Siliprandi |
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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 11209 | . 2 ⊢ ℝ ⊆ ℂ | |
2 | xpss12 5703 | . 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ)) | |
3 | 1, 1, 2 | mp2an 692 | 1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ) |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3962 × cxp 5686 ℂcc 11150 ℝcr 11151 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 ax-resscn 11209 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-ss 3979 df-opab 5210 df-xp 5694 |
This theorem is referenced by: ovolval2lem 46598 ovolval2 46599 ovolval3 46602 |
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