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Mirrors > Home > MPE Home > Th. List > ltrelpi | Structured version Visualization version GIF version |
Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ltrelpi | ⊢ <N ⊆ (N × N) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lti 9576 | . 2 ⊢ <N = ( E ∩ (N × N)) | |
2 | inss2 3796 | . 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N) | |
3 | 1, 2 | eqsstri 3598 | 1 ⊢ <N ⊆ (N × N) |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3539 ⊆ wss 3540 E cep 4947 × cxp 5036 Ncnpi 9545 <N clti 9548 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-in 3547 df-ss 3554 df-lti 9576 |
This theorem is referenced by: ltapi 9604 ltmpi 9605 nlt1pi 9607 indpi 9608 ordpipq 9643 ltsonq 9670 archnq 9681 |
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