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Mirrors > Home > ILE Home > Th. List > oprabex3 | Unicode version |
Description: Existence of an operation class abstraction (special case). (Contributed by NM, 19-Oct-2004.) |
Ref | Expression |
---|---|
oprabex3.1 | |
oprabex3.2 |
Ref | Expression |
---|---|
oprabex3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oprabex3.1 | . . 3 | |
2 | 1, 1 | xpex 4624 | . 2 |
3 | moeq 2832 | . . . . . 6 | |
4 | 3 | mosubop 4575 | . . . . 5 |
5 | 4 | mosubop 4575 | . . . 4 |
6 | anass 398 | . . . . . . . 8 | |
7 | 6 | 2exbii 1570 | . . . . . . 7 |
8 | 19.42vv 1865 | . . . . . . 7 | |
9 | 7, 8 | bitri 183 | . . . . . 6 |
10 | 9 | 2exbii 1570 | . . . . 5 |
11 | 10 | mobii 2014 | . . . 4 |
12 | 5, 11 | mpbir 145 | . . 3 |
13 | 12 | a1i 9 | . 2 |
14 | oprabex3.2 | . 2 | |
15 | 2, 2, 13, 14 | oprabex 5994 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 wex 1453 wcel 1465 wmo 1978 cvv 2660 cop 3500 cxp 4507 coprab 5743 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-coll 4013 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-oprab 5746 |
This theorem is referenced by: addvalex 7620 |
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