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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 6291 | . 2 ⊢ <N = ( E ∩ (N × N)) | |
2 | inss2 3152 | . 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N) | |
3 | 1, 2 | eqsstri 2969 | 1 ⊢ <N ⊆ (N × N) |
Colors of variables: wff set class |
Syntax hints: ∩ cin 2910 ⊆ wss 2911 E cep 4015 × cxp 4286 Ncnpi 6256 <N clti 6259 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-in 2918 df-ss 2925 df-lti 6291 |
This theorem is referenced by: ltsonq 6382 caucvgprlemk 6636 caucvgprlem1 6650 caucvgprlem2 6651 |
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