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Mirrors > Home > ILE Home > Th. List > dfer2 | Unicode version |
Description: Alternate definition of equivalence predicate. (Contributed by NM, 3-Jan-1997.) (Revised by Mario Carneiro, 12-Aug-2015.) |
Ref | Expression |
---|---|
dfer2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-er 6308 |
. 2
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2 | cnvsym 4830 |
. . . . 5
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3 | cotr 4828 |
. . . . 5
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4 | 2, 3 | anbi12i 449 |
. . . 4
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5 | unss 3177 |
. . . 4
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6 | 19.28v 1829 |
. . . . . . . 8
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7 | 6 | albii 1405 |
. . . . . . 7
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8 | 19.26 1416 |
. . . . . . 7
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9 | 7, 8 | bitri 183 |
. . . . . 6
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10 | 9 | albii 1405 |
. . . . 5
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11 | 19.26 1416 |
. . . . 5
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12 | 10, 11 | bitr2i 184 |
. . . 4
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13 | 4, 5, 12 | 3bitr3i 209 |
. . 3
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14 | 13 | 3anbi3i 1137 |
. 2
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15 | 1, 14 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3965 ax-pow 4017 ax-pr 4047 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2624 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-br 3854 df-opab 3908 df-xp 4460 df-rel 4461 df-cnv 4462 df-co 4463 df-er 6308 |
This theorem is referenced by: iserd 6334 |
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