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Mirrors > Home > MPE Home > Th. List > postr | Structured version Visualization version Unicode version |
Description: A poset ordering is transitive. (Contributed by NM, 11-Sep-2011.) |
Ref | Expression |
---|---|
posi.b | |
posi.l |
Ref | Expression |
---|---|
postr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | posi.b | . . 3 | |
2 | posi.l | . . 3 | |
3 | 1, 2 | posi 16950 | . 2 |
4 | 3 | simp3d 1075 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 class class class wbr 4653 cfv 5888 cbs 15857 cple 15948 cpo 16940 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-poset 16946 |
This theorem is referenced by: plttr 16970 joinle 17014 meetle 17028 lattr 17056 odupos 17135 omndadd2d 29708 omndadd2rd 29709 omndmul2 29712 atlatle 34607 cvratlem 34707 llncmp 34808 llncvrlpln 34844 lplncmp 34848 lplncvrlvol 34902 lvolcmp 34903 pmaple 35047 |
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