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Mirrors > Home > ILE Home > Th. List > cbviun | Unicode version |
Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 26-Mar-2006.) (Revised by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
cbviun.1 |
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cbviun.2 |
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cbviun.3 |
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Ref | Expression |
---|---|
cbviun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbviun.1 |
. . . . 5
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2 | 1 | nfcri 2276 |
. . . 4
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3 | cbviun.2 |
. . . . 5
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4 | 3 | nfcri 2276 |
. . . 4
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5 | cbviun.3 |
. . . . 5
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6 | 5 | eleq2d 2210 |
. . . 4
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7 | 2, 4, 6 | cbvrex 2654 |
. . 3
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8 | 7 | abbii 2256 |
. 2
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9 | df-iun 3823 |
. 2
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10 | df-iun 3823 |
. 2
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11 | 8, 9, 10 | 3eqtr4i 2171 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-iun 3823 |
This theorem is referenced by: cbviunv 3860 funiunfvdmf 5673 mpomptsx 6103 dmmpossx 6105 fmpox 6106 fsum2dlemstep 11235 fisumcom2 11239 fsumiun 11278 ctiunctlemf 11987 ctiunctal 11990 |
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