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Mirrors > Home > ILE Home > Th. List > dfrel2 | Unicode version |
Description: Alternate definition of relation. Exercise 2 of [TakeutiZaring] p. 25. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
dfrel2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relcnv 4912 | . . 3 | |
2 | vex 2684 | . . . . . 6 | |
3 | vex 2684 | . . . . . 6 | |
4 | 2, 3 | opelcnv 4716 | . . . . 5 |
5 | 3, 2 | opelcnv 4716 | . . . . 5 |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | eqrelriv 4627 | . . 3 |
8 | 1, 7 | mpan 420 | . 2 |
9 | releq 4616 | . . 3 | |
10 | 1, 9 | mpbii 147 | . 2 |
11 | 8, 10 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 cop 3525 ccnv 4533 wrel 4539 |
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-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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-rel 4541 df-cnv 4542 |
This theorem is referenced by: dfrel4v 4985 cnvcnv 4986 cnveqb 4989 dfrel3 4991 cnvcnvres 4997 cnvsn 5016 cores2 5046 co01 5048 coi2 5050 relcnvtr 5053 relcnvexb 5073 funcnvres2 5193 f1cnvcnv 5334 f1ocnv 5373 f1ocnvb 5374 f1ococnv1 5389 isores1 5708 cnvf1o 6115 tposf12 6159 ssenen 6738 relcnvfi 6822 caseinl 6969 caseinr 6970 fsumcnv 11199 structcnvcnv 11964 hmeocnv 12465 hmeocnvb 12476 |
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