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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relcnv 4925 |
. . 3
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2 | vex 2692 |
. . . . . 6
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3 | vex 2692 |
. . . . . 6
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4 | 2, 3 | opelcnv 4729 |
. . . . 5
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5 | 3, 2 | opelcnv 4729 |
. . . . 5
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6 | 4, 5 | bitri 183 |
. . . 4
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7 | 6 | eqrelriv 4640 |
. . 3
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8 | 1, 7 | mpan 421 |
. 2
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9 | releq 4629 |
. . 3
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10 | 1, 9 | mpbii 147 |
. 2
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11 | 8, 10 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-rel 4554 df-cnv 4555 |
This theorem is referenced by: dfrel4v 4998 cnvcnv 4999 cnveqb 5002 dfrel3 5004 cnvcnvres 5010 cnvsn 5029 cores2 5059 co01 5061 coi2 5063 relcnvtr 5066 relcnvexb 5086 funcnvres2 5206 f1cnvcnv 5347 f1ocnv 5388 f1ocnvb 5389 f1ococnv1 5404 isores1 5723 cnvf1o 6130 tposf12 6174 ssenen 6753 relcnvfi 6837 caseinl 6984 caseinr 6985 fsumcnv 11238 structcnvcnv 12014 hmeocnv 12515 hmeocnvb 12526 |
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