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Mirrors > Home > ILE Home > Th. List > ertr3d | Unicode version |
Description: A transitivity relation for equivalences. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
ersymb.1 |
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ertr3d.5 |
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ertr3d.6 |
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Ref | Expression |
---|---|
ertr3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ersymb.1 |
. 2
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2 | ertr3d.5 |
. . 3
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3 | 1, 2 | ersym 6392 |
. 2
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4 | ertr3d.6 |
. 2
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5 | 1, 3, 4 | ertrd 6396 |
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 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-br 3894 df-opab 3948 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-er 6380 |
This theorem is referenced by: xmetresbl 12422 |
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