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Mirrors > Home > ILE Home > Th. List > rexeqbidv | Unicode version |
Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 6-Nov-2007.) |
Ref | Expression |
---|---|
raleqbidv.1 |
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raleqbidv.2 |
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Ref | Expression |
---|---|
rexeqbidv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleqbidv.1 |
. . 3
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2 | 1 | rexeqdv 2679 |
. 2
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3 | raleqbidv.2 |
. . 3
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4 | 3 | rexbidv 2478 |
. 2
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5 | 2, 4 | bitrd 188 |
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-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 |
This theorem is referenced by: supeq123d 6984 ismnddef 12708 mndpropd 12730 mnd1 12734 isgrp 12770 isgrpd2e 12783 grp1 12862 issrgid 12987 isringid 13031 reldvdsrsrg 13083 dvdsrvald 13084 |
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