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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 11169 | . 2 ⊢ ℝ ⊆ ℂ | |
2 | xpss12 5691 | . 2 ⊢ ((ℝ ⊆ ℂ ∧ ℝ ⊆ ℂ) → (ℝ × ℝ) ⊆ (ℂ × ℂ)) | |
3 | 1, 1, 2 | mp2an 690 | 1 ⊢ (ℝ × ℝ) ⊆ (ℂ × ℂ) |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3948 × cxp 5674 ℂcc 11110 ℝcr 11111 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 ax-resscn 11169 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-v 3476 df-in 3955 df-ss 3965 df-opab 5211 df-xp 5682 |
This theorem is referenced by: ovolval2lem 45438 ovolval2 45439 ovolval3 45442 |
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