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Mirrors > Home > ILE Home > Th. List > cnv0 | Unicode version |
Description: The converse of the empty set. (Contributed by NM, 6-Apr-1998.) |
Ref | Expression |
---|---|
cnv0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relcnv 4887 | . 2 | |
2 | rel0 4634 | . 2 | |
3 | vex 2663 | . . . 4 | |
4 | vex 2663 | . . . 4 | |
5 | 3, 4 | opelcnv 4691 | . . 3 |
6 | noel 3337 | . . . 4 | |
7 | noel 3337 | . . . 4 | |
8 | 6, 7 | 2false 675 | . . 3 |
9 | 5, 8 | bitr4i 186 | . 2 |
10 | 1, 2, 9 | eqrelriiv 4603 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 c0 3333 cop 3500 ccnv 4508 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 |
This theorem is referenced by: xp0 4928 cnveq0 4965 co01 5023 f10 5369 f1o00 5370 tpos0 6139 |
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