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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 2475 | . . 3 |
3 | 2 | cbvralv 2701 | . 2 |
4 | cbvral2v.2 | . . . 4 | |
5 | 4 | cbvralv 2701 | . . 3 |
6 | 5 | ralbii 2481 | . 2 |
7 | 3, 6 | bitri 184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 105 wral 2453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1459 df-sb 1761 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ral 2458 |
This theorem is referenced by: cbvral3v 2716 fununi 5276 fiintim 6918 isoti 6996 nninfwlpoim 7166 cauappcvgprlemlim 7635 caucvgprlemnkj 7640 caucvgprlemcl 7650 caucvgprprlemcbv 7661 axcaucvglemcau 7872 axpre-suploc 7876 seqvalcd 10427 seqovcd 10431 seq3distr 10481 fprodcl2lem 11580 ennnfonelemr 12390 ctinf 12397 grppropd 12754 |
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