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Mirrors > Home > ILE Home > Th. List > 2ecoptocl | Unicode version |
Description: Implicit substitution of classes for equivalence classes of ordered pairs. (Contributed by NM, 23-Jul-1995.) |
Ref | Expression |
---|---|
2ecoptocl.1 | |
2ecoptocl.2 | |
2ecoptocl.3 | |
2ecoptocl.4 |
Ref | Expression |
---|---|
2ecoptocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2ecoptocl.1 | . . 3 | |
2 | 2ecoptocl.3 | . . . 4 | |
3 | 2 | imbi2d 228 | . . 3 |
4 | 2ecoptocl.2 | . . . . . 6 | |
5 | 4 | imbi2d 228 | . . . . 5 |
6 | 2ecoptocl.4 | . . . . . 6 | |
7 | 6 | ex 113 | . . . . 5 |
8 | 1, 5, 7 | ecoptocl 6216 | . . . 4 |
9 | 8 | com12 30 | . . 3 |
10 | 1, 3, 9 | ecoptocl 6216 | . 2 |
11 | 10 | impcom 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 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: 3ecoptocl 6218 ecovcom 6236 ecovicom 6237 addclnq 6565 mulclnq 6566 nqtri3or 6586 ltexnqq 6598 addclnq0 6641 mulclnq0 6642 distrnq0 6649 mulcomnq0 6650 addassnq0 6652 addclsr 6930 mulclsr 6931 mulgt0sr 6954 aptisr 6955 |
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