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Mirrors > Home > ILE Home > Th. List > cnvti | Unicode version |
Description: If a relation satisfies a condition corresponding to tightness of an apartness generated by an order, so does its converse. (Contributed by Jim Kingdon, 17-Dec-2021.) |
Ref | Expression |
---|---|
eqinfti.ti |
Ref | Expression |
---|---|
cnvti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqinfti.ti | . . 3 | |
2 | ancom 264 | . . 3 | |
3 | 1, 2 | syl6bb 195 | . 2 |
4 | brcnvg 4720 | . . . . 5 | |
5 | 4 | notbid 656 | . . . 4 |
6 | brcnvg 4720 | . . . . . 6 | |
7 | 6 | ancoms 266 | . . . . 5 |
8 | 7 | notbid 656 | . . . 4 |
9 | 5, 8 | anbi12d 464 | . . 3 |
10 | 9 | adantl 275 | . 2 |
11 | 3, 10 | bitr4d 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 1480 class class class wbr 3929 ccnv 4538 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-cnv 4547 |
This theorem is referenced by: eqinfti 6907 infvalti 6909 infclti 6910 inflbti 6911 infglbti 6912 infmoti 6915 infsnti 6917 infisoti 6919 infrenegsupex 9389 infxrnegsupex 11032 |
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