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Mirrors > Home > ILE Home > Th. List > opabid | Unicode version |
Description: The law of concretion. Special case of Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
opabid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2663 | . . 3 | |
2 | vex 2663 | . . 3 | |
3 | 1, 2 | opex 4121 | . 2 |
4 | copsexg 4136 | . . 3 | |
5 | 4 | bicomd 140 | . 2 |
6 | df-opab 3960 | . 2 | |
7 | 3, 5, 6 | elab2 2805 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 cop 3500 copab 3958 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
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-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-opab 3960 |
This theorem is referenced by: opelopabsb 4152 ssopab2b 4168 dmopab 4720 rnopab 4756 funopab 5128 funco 5133 fvmptss2 5464 f1ompt 5539 ovid 5855 enssdom 6624 |
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