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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 229 | . . . 4 |
4 | 3ecoptocl.4 | . . . . 5 | |
5 | 4 | imbi2d 229 | . . . 4 |
6 | 3ecoptocl.2 | . . . . . . 7 | |
7 | 6 | imbi2d 229 | . . . . . 6 |
8 | 3ecoptocl.5 | . . . . . . 7 | |
9 | 8 | 3expib 1201 | . . . . . 6 |
10 | 1, 7, 9 | ecoptocl 6600 | . . . . 5 |
11 | 10 | com12 30 | . . . 4 |
12 | 1, 3, 5, 11 | 2ecoptocl 6601 | . . 3 |
13 | 12 | com12 30 | . 2 |
14 | 13 | 3impib 1196 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wceq 1348 wcel 2141 cop 3586 cxp 4609 cec 6511 cqs 6512 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 df-ec 6515 df-qs 6519 |
This theorem is referenced by: ecovass 6622 ecoviass 6623 ecovdi 6624 ecovidi 6625 ltsonq 7360 ltanqg 7362 ltmnqg 7363 lttrsr 7724 ltsosr 7726 ltasrg 7732 mulextsr1 7743 |
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