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Mirrors > Home > ILE Home > Th. List > ltrelpi | GIF version |
Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
ltrelpi | ⊢ <N ⊆ (N × N) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lti 7083 | . 2 ⊢ <N = ( E ∩ (N × N)) | |
2 | inss2 3267 | . 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N) | |
3 | 1, 2 | eqsstri 3099 | 1 ⊢ <N ⊆ (N × N) |
Colors of variables: wff set class |
Syntax hints: ∩ cin 3040 ⊆ wss 3041 E cep 4179 × cxp 4507 Ncnpi 7048 <N clti 7051 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-lti 7083 |
This theorem is referenced by: ltsonq 7174 caucvgprlemk 7441 caucvgprlem1 7455 caucvgprlem2 7456 caucvgprprlemk 7459 caucvgprprlemval 7464 caucvgprprlem1 7485 caucvgprprlem2 7486 ltrenn 7631 |
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