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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 2907 | . 2 | |
2 | dfsbcq2 2907 | . . 3 | |
3 | 2 | reubidv 2612 | . 2 |
4 | nfcv 2279 | . . . 4 | |
5 | nfs1v 1910 | . . . 4 | |
6 | 4, 5 | nfreuxy 2603 | . . 3 |
7 | sbequ12 1744 | . . . 4 | |
8 | 7 | reubidv 2612 | . . 3 |
9 | 6, 8 | sbie 1764 | . 2 |
10 | 1, 3, 9 | vtoclbg 2742 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 wsb 1735 wreu 2416 wsbc 2904 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-reu 2421 df-v 2683 df-sbc 2905 |
This theorem is referenced by: (None) |
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