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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 4989 | . . 3 | |
2 | vex 2733 | . . . . . 6 | |
3 | vex 2733 | . . . . . 6 | |
4 | 2, 3 | opelcnv 4793 | . . . . 5 |
5 | 3, 2 | opelcnv 4793 | . . . . 5 |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | eqrelriv 4704 | . . 3 |
8 | 1, 7 | mpan 422 | . 2 |
9 | releq 4693 | . . 3 | |
10 | 1, 9 | mpbii 147 | . 2 |
11 | 8, 10 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1348 wcel 2141 cop 3586 ccnv 4610 wrel 4616 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-rel 4618 df-cnv 4619 |
This theorem is referenced by: dfrel4v 5062 cnvcnv 5063 cnveqb 5066 dfrel3 5068 cnvcnvres 5074 cnvsn 5093 cores2 5123 co01 5125 coi2 5127 relcnvtr 5130 relcnvexb 5150 funcnvres2 5273 f1cnvcnv 5414 f1ocnv 5455 f1ocnvb 5456 f1ococnv1 5471 isores1 5793 cnvf1o 6204 tposf12 6248 ssenen 6829 relcnvfi 6918 caseinl 7068 caseinr 7069 fsumcnv 11400 fprodcnv 11588 structcnvcnv 12432 hmeocnv 13101 hmeocnvb 13112 |
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