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Mirrors > Home > ILE Home > Th. List > isprm | Unicode version |
Description: The predicate "is a prime number". A prime number is a positive integer with exactly two positive divisors. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
isprm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 3928 | . . . 4 | |
2 | 1 | rabbidv 2670 | . . 3 |
3 | 2 | breq1d 3934 | . 2 |
4 | df-prm 11778 | . 2 | |
5 | 3, 4 | elrab2 2838 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wcel 1480 crab 2418 class class class wbr 3924 c2o 6300 cen 6625 cn 8713 cdvds 11482 cprime 11777 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rab 2423 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-prm 11778 |
This theorem is referenced by: prmnn 11780 1nprm 11784 isprm2 11787 |
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