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Mirrors > Home > ILE Home > Th. List > cbvral2v | Unicode version |
Description: Change bound variables of double restricted universal quantification, using implicit substitution. (Contributed by NM, 10-Aug-2004.) |
Ref | Expression |
---|---|
cbvral2v.1 | |
cbvral2v.2 |
Ref | Expression |
---|---|
cbvral2v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvral2v.1 | . . . 4 | |
2 | 1 | ralbidv 2368 | . . 3 |
3 | 2 | cbvralv 2577 | . 2 |
4 | cbvral2v.2 | . . . 4 | |
5 | 4 | cbvralv 2577 | . . 3 |
6 | 5 | ralbii 2372 | . 2 |
7 | 3, 6 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wral 2348 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 |
This theorem is referenced by: cbvral3v 2587 fununi 4987 isoti 6420 cauappcvgprlemlim 6851 caucvgprlemnkj 6856 caucvgprlemcl 6866 caucvgprprlemcbv 6877 axcaucvglemcau 7064 iseqdistr 9470 |
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