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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 2949 | . 2 | |
2 | dfsbcq2 2949 | . . 3 | |
3 | 2 | ralbidv 2464 | . 2 |
4 | nfcv 2306 | . . . 4 | |
5 | nfs1v 1926 | . . . 4 | |
6 | 4, 5 | nfralxy 2502 | . . 3 |
7 | sbequ12 1758 | . . . 4 | |
8 | 7 | ralbidv 2464 | . . 3 |
9 | 6, 8 | sbie 1778 | . 2 |
10 | 1, 3, 9 | vtoclbg 2782 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wsb 1749 wcel 2135 wral 2442 wsbc 2946 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2723 df-sbc 2947 |
This theorem is referenced by: r19.12sn 3636 |
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