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Mirrors > Home > ILE Home > Th. List > ralxfr2d | Unicode version |
Description: Transfer universal
quantification from a variable ![]() ![]() ![]() |
Ref | Expression |
---|---|
ralxfr2d.1 |
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ralxfr2d.2 |
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ralxfr2d.3 |
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Ref | Expression |
---|---|
ralxfr2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfr2d.1 |
. . . 4
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2 | elisset 2766 |
. . . 4
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3 | 1, 2 | syl 14 |
. . 3
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4 | ralxfr2d.2 |
. . . . . . . 8
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5 | 4 | biimprd 158 |
. . . . . . 7
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6 | r19.23v 2599 |
. . . . . . 7
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7 | 5, 6 | sylibr 134 |
. . . . . 6
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8 | 7 | r19.21bi 2578 |
. . . . 5
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9 | eleq1 2252 |
. . . . 5
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10 | 8, 9 | mpbidi 151 |
. . . 4
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11 | 10 | exlimdv 1830 |
. . 3
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12 | 3, 11 | mpd 13 |
. 2
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13 | 4 | biimpa 296 |
. 2
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14 | ralxfr2d.3 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 12, 13, 14 | ralxfrd 4480 |
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-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 |
This theorem is referenced by: ralrn 5675 ralima 5777 cnrest2 14196 cnptoprest2 14200 |
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