Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 219 | . . . 4 |
4 | 3ecoptocl.4 | . . . . 5 | |
5 | 4 | imbi2d 219 | . . . 4 |
6 | 3ecoptocl.2 | . . . . . . 7 | |
7 | 6 | imbi2d 219 | . . . . . 6 |
8 | 3ecoptocl.5 | . . . . . . 7 | |
9 | 8 | 3expib 1107 | . . . . . 6 |
10 | 1, 7, 9 | ecoptocl 6193 | . . . . 5 |
11 | 10 | com12 27 | . . . 4 |
12 | 1, 3, 5, 11 | 2ecoptocl 6194 | . . 3 |
13 | 12 | com12 27 | . 2 |
14 | 13 | 3impib 1102 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 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: ecovass 6215 ecoviass 6216 ecovdi 6217 ecovidi 6218 ltsonq 6496 ltanqg 6498 ltmnqg 6499 lttrsr 6847 ltsosr 6849 ltasrg 6855 mulextsr1 6865 |
Copyright terms: Public domain | W3C validator |