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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 230 |
. . . 4
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4 | 3ecoptocl.4 |
. . . . 5
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5 | 4 | imbi2d 230 |
. . . 4
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6 | 3ecoptocl.2 |
. . . . . . 7
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7 | 6 | imbi2d 230 |
. . . . . 6
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8 | 3ecoptocl.5 |
. . . . . . 7
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9 | 8 | 3expib 1208 |
. . . . . 6
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10 | 1, 7, 9 | ecoptocl 6648 |
. . . . 5
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11 | 10 | com12 30 |
. . . 4
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12 | 1, 3, 5, 11 | 2ecoptocl 6649 |
. . 3
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13 | 12 | com12 30 |
. 2
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14 | 13 | 3impib 1203 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-ec 6561 df-qs 6565 |
This theorem is referenced by: ecovass 6670 ecoviass 6671 ecovdi 6672 ecovidi 6673 ltsonq 7427 ltanqg 7429 ltmnqg 7430 lttrsr 7791 ltsosr 7793 ltasrg 7799 mulextsr1 7810 |
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