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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 7303 | . 2 ⊢ <N = ( E ∩ (N × N)) | |
2 | inss2 3356 | . 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N) | |
3 | 1, 2 | eqsstri 3187 | 1 ⊢ <N ⊆ (N × N) |
Colors of variables: wff set class |
Syntax hints: ∩ cin 3128 ⊆ wss 3129 E cep 4286 × cxp 4623 Ncnpi 7268 <N clti 7271 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-lti 7303 |
This theorem is referenced by: ltsonq 7394 caucvgprlemk 7661 caucvgprlem1 7675 caucvgprlem2 7676 caucvgprprlemk 7679 caucvgprprlemval 7684 caucvgprprlem1 7705 caucvgprprlem2 7706 ltrenn 7851 |
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