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Mirrors > Home > ILE Home > Th. List > reex | GIF version |
Description: The real numbers form a set. (Contributed by Mario Carneiro, 17-Nov-2014.) |
Ref | Expression |
---|---|
reex | ⊢ ℝ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7768 | . 2 ⊢ ℂ ∈ V | |
2 | ax-resscn 7736 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | ssexi 4074 | 1 ⊢ ℝ ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1481 Vcvv 2689 ℂcc 7642 ℝcr 7643 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-cnex 7735 ax-resscn 7736 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-in 3082 df-ss 3089 |
This theorem is referenced by: reelprrecn 7779 peano5nni 8747 xrex 9669 iccen 9819 sqrtrval 10804 absval 10805 negfi 11031 climrecvg1n 11149 ismet 12552 rerestcntop 12758 dvcjbr 12880 dvcj 12881 dvfre 12882 dceqnconst 13423 iooreen 13427 |
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