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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 7269 | . 2 ⊢ <N = ( E ∩ (N × N)) | |
2 | inss2 3348 | . 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N) | |
3 | 1, 2 | eqsstri 3179 | 1 ⊢ <N ⊆ (N × N) |
Colors of variables: wff set class |
Syntax hints: ∩ cin 3120 ⊆ wss 3121 E cep 4272 × cxp 4609 Ncnpi 7234 <N clti 7237 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-in 3127 df-ss 3134 df-lti 7269 |
This theorem is referenced by: ltsonq 7360 caucvgprlemk 7627 caucvgprlem1 7641 caucvgprlem2 7642 caucvgprprlemk 7645 caucvgprprlemval 7650 caucvgprprlem1 7671 caucvgprprlem2 7672 ltrenn 7817 |
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