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Mirrors > Home > ILE Home > Th. List > sbcralg | Unicode version |
Description: Interchange class substitution and restricted quantifier. (Contributed by NM, 15-Nov-2005.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
sbcralg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 2767 | . 2 | |
2 | dfsbcq2 2767 | . . 3 | |
3 | 2 | ralbidv 2326 | . 2 |
4 | nfcv 2178 | . . . 4 | |
5 | nfs1v 1815 | . . . 4 | |
6 | 4, 5 | nfralxy 2360 | . . 3 |
7 | sbequ12 1654 | . . . 4 | |
8 | 7 | ralbidv 2326 | . . 3 |
9 | 6, 8 | sbie 1674 | . 2 |
10 | 1, 3, 9 | vtoclbg 2614 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wsb 1645 wral 2306 wsbc 2764 |
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-ral 2311 df-v 2559 df-sbc 2765 |
This theorem is referenced by: r19.12sn 3436 |
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