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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 |
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cbvral2v.2 |
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Ref | Expression |
---|---|
cbvral2v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvral2v.1 |
. . . 4
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2 | 1 | ralbidv 2490 |
. . 3
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3 | 2 | cbvralv 2718 |
. 2
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4 | cbvral2v.2 |
. . . 4
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5 | 4 | cbvralv 2718 |
. . 3
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6 | 5 | ralbii 2496 |
. 2
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7 | 3, 6 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 |
This theorem is referenced by: cbvral3v 2733 fununi 5306 fiintim 6961 isoti 7040 nninfwlpoim 7211 cauappcvgprlemlim 7695 caucvgprlemnkj 7700 caucvgprlemcl 7710 caucvgprprlemcbv 7721 axcaucvglemcau 7932 axpre-suploc 7936 seqvalcd 10498 seqovcd 10502 seq3distr 10553 fprodcl2lem 11654 ennnfonelemr 12485 ctinf 12492 ercpbl 12818 grppropd 12985 |
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