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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 | |
3ecoptocl.2 | |
3ecoptocl.3 | |
3ecoptocl.4 | |
3ecoptocl.5 |
Ref | Expression |
---|---|
3ecoptocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ecoptocl.1 | . . . 4 | |
2 | 3ecoptocl.3 | . . . . 5 | |
3 | 2 | imbi2d 228 | . . . 4 |
4 | 3ecoptocl.4 | . . . . 5 | |
5 | 4 | imbi2d 228 | . . . 4 |
6 | 3ecoptocl.2 | . . . . . . 7 | |
7 | 6 | imbi2d 228 | . . . . . 6 |
8 | 3ecoptocl.5 | . . . . . . 7 | |
9 | 8 | 3expib 1141 | . . . . . 6 |
10 | 1, 7, 9 | ecoptocl 6216 | . . . . 5 |
11 | 10 | com12 30 | . . . 4 |
12 | 1, 3, 5, 11 | 2ecoptocl 6217 | . . 3 |
13 | 12 | com12 30 | . 2 |
14 | 13 | 3impib 1136 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wcel 1433 cop 3401 cxp 4361 cec 6127 cqs 6128 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-ec 6131 df-qs 6135 |
This theorem is referenced by: ecovass 6238 ecoviass 6239 ecovdi 6240 ecovidi 6241 ltsonq 6588 ltanqg 6590 ltmnqg 6591 lttrsr 6939 ltsosr 6941 ltasrg 6947 mulextsr1 6957 |
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