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Mirrors > Home > ILE Home > Th. List > 3ecoptocl | Unicode version |
Description: Implicit substitution of classes for equivalence classes of ordered pairs. (Contributed by NM, 9-Aug-1995.) |
Ref | Expression |
---|---|
3ecoptocl.1 |
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3ecoptocl.2 |
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3ecoptocl.3 |
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3ecoptocl.4 |
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3ecoptocl.5 |
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Ref | Expression |
---|---|
3ecoptocl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ecoptocl.1 |
. . . 4
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2 | 3ecoptocl.3 |
. . . . 5
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3 | 2 | imbi2d 228 |
. . . 4
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4 | 3ecoptocl.4 |
. . . . 5
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5 | 4 | imbi2d 228 |
. . . 4
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6 | 3ecoptocl.2 |
. . . . . . 7
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7 | 6 | imbi2d 228 |
. . . . . 6
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8 | 3ecoptocl.5 |
. . . . . . 7
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9 | 8 | 3expib 1146 |
. . . . . 6
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10 | 1, 7, 9 | ecoptocl 6377 |
. . . . 5
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11 | 10 | com12 30 |
. . . 4
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12 | 1, 3, 5, 11 | 2ecoptocl 6378 |
. . 3
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13 | 12 | com12 30 |
. 2
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14 | 13 | 3impib 1141 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 df-opab 3900 df-xp 4444 df-cnv 4446 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-ec 6292 df-qs 6296 |
This theorem is referenced by: ecovass 6399 ecoviass 6400 ecovdi 6401 ecovidi 6402 ltsonq 6955 ltanqg 6957 ltmnqg 6958 lttrsr 7306 ltsosr 7308 ltasrg 7314 mulextsr1 7324 |
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