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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 4966 | . . 3 | |
2 | vex 2715 | . . . . . 6 | |
3 | vex 2715 | . . . . . 6 | |
4 | 2, 3 | opelcnv 4770 | . . . . 5 |
5 | 3, 2 | opelcnv 4770 | . . . . 5 |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | eqrelriv 4681 | . . 3 |
8 | 1, 7 | mpan 421 | . 2 |
9 | releq 4670 | . . 3 | |
10 | 1, 9 | mpbii 147 | . 2 |
11 | 8, 10 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 wcel 2128 cop 3564 ccnv 4587 wrel 4593 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4028 df-xp 4594 df-rel 4595 df-cnv 4596 |
This theorem is referenced by: dfrel4v 5039 cnvcnv 5040 cnveqb 5043 dfrel3 5045 cnvcnvres 5051 cnvsn 5070 cores2 5100 co01 5102 coi2 5104 relcnvtr 5107 relcnvexb 5127 funcnvres2 5247 f1cnvcnv 5388 f1ocnv 5429 f1ocnvb 5430 f1ococnv1 5445 isores1 5766 cnvf1o 6174 tposf12 6218 ssenen 6798 relcnvfi 6887 caseinl 7037 caseinr 7038 fsumcnv 11345 fprodcnv 11533 structcnvcnv 12276 hmeocnv 12777 hmeocnvb 12788 |
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