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Mirrors > Home > ILE Home > Th. List > cbvixp | Unicode version |
Description: Change bound variable in an indexed Cartesian product. (Contributed by Jeff Madsen, 20-Jun-2011.) |
Ref | Expression |
---|---|
cbvixp.1 |
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cbvixp.2 |
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cbvixp.3 |
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Ref | Expression |
---|---|
cbvixp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvixp.1 |
. . . . . 6
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2 | 1 | nfel2 2349 |
. . . . 5
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3 | cbvixp.2 |
. . . . . 6
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4 | 3 | nfel2 2349 |
. . . . 5
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5 | fveq2 5554 |
. . . . . 6
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6 | cbvixp.3 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | eleq12d 2264 |
. . . . 5
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8 | 2, 4, 7 | cbvral 2722 |
. . . 4
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9 | 8 | anbi2i 457 |
. . 3
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10 | 9 | abbii 2309 |
. 2
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11 | dfixp 6754 |
. 2
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12 | dfixp 6754 |
. 2
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13 | 10, 11, 12 | 3eqtr4i 2224 |
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 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-br 4030 df-iota 5215 df-fn 5257 df-fv 5262 df-ixp 6753 |
This theorem is referenced by: cbvixpv 6770 mptelixpg 6788 |
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