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Mirrors > Home > ILE Home > Th. List > sbcreug | Unicode version |
Description: Interchange class substitution and restricted unique existential quantifier. (Contributed by NM, 24-Feb-2013.) |
Ref | Expression |
---|---|
sbcreug |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 2940 | . 2 | |
2 | dfsbcq2 2940 | . . 3 | |
3 | 2 | reubidv 2640 | . 2 |
4 | nfcv 2299 | . . . 4 | |
5 | nfs1v 1919 | . . . 4 | |
6 | 4, 5 | nfreuxy 2631 | . . 3 |
7 | sbequ12 1751 | . . . 4 | |
8 | 7 | reubidv 2640 | . . 3 |
9 | 6, 8 | sbie 1771 | . 2 |
10 | 1, 3, 9 | vtoclbg 2773 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wsb 1742 wcel 2128 wreu 2437 wsbc 2937 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-reu 2442 df-v 2714 df-sbc 2938 |
This theorem is referenced by: (None) |
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