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Mirrors > Home > ILE Home > Th. List > elni | Unicode version |
Description: Membership in the class of positive integers. (Contributed by NM, 15-Aug-1995.) |
Ref | Expression |
---|---|
elni |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ni 7320 |
. . 3
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2 | 1 | eleq2i 2255 |
. 2
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3 | eldifsn 3733 |
. 2
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4 | 2, 3 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ne 2360 df-v 2753 df-dif 3145 df-sn 3612 df-ni 7320 |
This theorem is referenced by: 0npi 7329 elni2 7330 1pi 7331 addclpi 7343 mulclpi 7344 nlt1pig 7357 indpi 7358 nqnq0pi 7454 prarloclemcalc 7518 |
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