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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 8960 | . 2 ⊢ ℕ ∈ V | |
2 | prmssnn 12155 | . 2 ⊢ ℙ ⊆ ℕ | |
3 | 1, 2 | ssexi 4159 | 1 ⊢ ℙ ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2752 ℕcn 8954 ℙcprime 12150 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4139 ax-cnex 7937 ax-resscn 7938 ax-1re 7940 ax-addrcl 7943 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3616 df-pr 3617 df-op 3619 df-int 3863 df-br 4022 df-inn 8955 df-prm 12151 |
This theorem is referenced by: 1arithlem1 12406 1arith 12410 |
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