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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 219 | . . 3 |
4 | 2ecoptocl.2 | . . . . . 6 | |
5 | 4 | imbi2d 219 | . . . . 5 |
6 | 2ecoptocl.4 | . . . . . 6 | |
7 | 6 | ex 108 | . . . . 5 |
8 | 1, 5, 7 | ecoptocl 6193 | . . . 4 |
9 | 8 | com12 27 | . . 3 |
10 | 1, 3, 9 | ecoptocl 6193 | . 2 |
11 | 10 | impcom 116 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 cop 3378 cxp 4343 cec 6104 cqs 6105 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-ec 6108 df-qs 6112 |
This theorem is referenced by: 3ecoptocl 6195 ecovcom 6213 ecovicom 6214 addclnq 6473 mulclnq 6474 nqtri3or 6494 ltexnqq 6506 addclnq0 6549 mulclnq0 6550 distrnq0 6557 mulcomnq0 6558 addassnq0 6560 addclsr 6838 mulclsr 6839 mulgt0sr 6862 aptisr 6863 |
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