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Mirrors > Home > ILE Home > Th. List > prmex | GIF version |
Description: The set of prime numbers exists. (Contributed by AV, 22-Jul-2020.) |
Ref | Expression |
---|---|
prmex | ⊢ ℙ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnex 8340 | . 2 ⊢ ℕ ∈ V | |
2 | prmssnn 10888 | . 2 ⊢ ℙ ⊆ ℕ | |
3 | 1, 2 | ssexi 3945 | 1 ⊢ ℙ ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1436 Vcvv 2614 ℕcn 8334 ℙcprime 10883 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 ax-cnex 7357 ax-resscn 7358 ax-1re 7360 ax-addrcl 7363 |
This theorem depends on definitions: df-bi 115 df-3an 924 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ral 2360 df-rab 2364 df-v 2616 df-un 2990 df-in 2992 df-ss 2999 df-sn 3431 df-pr 3432 df-op 3434 df-int 3666 df-br 3815 df-inn 8335 df-prm 10884 |
This theorem is referenced by: (None) |
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