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Mirrors > Home > ILE Home > Th. List > ceqsrexv | Unicode version |
Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 30-Apr-2004.) |
Ref | Expression |
---|---|
ceqsrexv.1 |
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Ref | Expression |
---|---|
ceqsrexv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2461 |
. . 3
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2 | an12 561 |
. . . 4
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3 | 2 | exbii 1605 |
. . 3
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4 | 1, 3 | bitr4i 187 |
. 2
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5 | eleq1 2240 |
. . . . 5
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6 | ceqsrexv.1 |
. . . . 5
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7 | 5, 6 | anbi12d 473 |
. . . 4
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8 | 7 | ceqsexgv 2868 |
. . 3
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9 | 8 | bianabs 611 |
. 2
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10 | 4, 9 | bitrid 192 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2741 |
This theorem is referenced by: ceqsrexbv 2870 ceqsrex2v 2871 f1oiso 5829 creur 8918 creui 8919 |
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