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Mirrors > Home > ILE Home > Th. List > ralxfrd | Unicode version |
Description: Transfer universal
quantification from a variable ![]() ![]() ![]() |
Ref | Expression |
---|---|
ralxfrd.1 |
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ralxfrd.2 |
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ralxfrd.3 |
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Ref | Expression |
---|---|
ralxfrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfrd.1 |
. . . 4
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2 | ralxfrd.3 |
. . . . 5
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3 | 2 | adantlr 469 |
. . . 4
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4 | 1, 3 | rspcdv 2796 |
. . 3
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5 | 4 | ralrimdva 2515 |
. 2
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6 | ralxfrd.2 |
. . . 4
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7 | r19.29 2572 |
. . . . 5
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8 | 2 | biimprd 157 |
. . . . . . . . 9
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9 | 8 | expimpd 361 |
. . . . . . . 8
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10 | 9 | ancomsd 267 |
. . . . . . 7
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11 | 10 | ad2antrr 480 |
. . . . . 6
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12 | 11 | rexlimdva 2552 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 7, 12 | syl5 32 |
. . . 4
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14 | 6, 13 | mpan2d 425 |
. . 3
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15 | 14 | ralrimdva 2515 |
. 2
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16 | 5, 15 | impbid 128 |
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-ral 2422 df-rex 2423 df-v 2691 |
This theorem is referenced by: ralxfr2d 4393 ralxfr 4395 |
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