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Mirrors > Home > ILE Home > Th. List > elab | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
elab.1 | |
elab.2 |
Ref | Expression |
---|---|
elab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . 2 | |
2 | elab.1 | . 2 | |
3 | elab.2 | . 2 | |
4 | 1, 2, 3 | elabf 2686 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 cab 2026 cvv 2557 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: ralab 2701 rexab 2703 intab 3644 dfiin2g 3690 dfiunv2 3693 uniuni 4183 peano5 4321 finds 4323 finds2 4324 funcnvuni 4968 fun11iun 5147 elabrex 5397 abrexco 5398 indpi 6440 nqprm 6640 nqprrnd 6641 nqprdisj 6642 nqprloc 6643 nqprl 6649 nqpru 6650 cauappcvgprlem2 6758 caucvgprlem2 6778 peano1nnnn 6928 peano2nnnn 6929 1nn 7925 peano2nn 7926 dfuzi 8348 shftfvalg 9419 ovshftex 9420 shftfval 9422 bj-ssom 10060 |
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