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Mirrors > Home > ILE Home > Th. List > rexeqdv | Unicode version |
Description: Equality deduction for restricted existential quantifier. (Contributed by NM, 14-Jan-2007.) |
Ref | Expression |
---|---|
raleq1d.1 |
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Ref | Expression |
---|---|
rexeqdv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq1d.1 |
. 2
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2 | rexeq 2673 |
. 2
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3 | 1, 2 | syl 14 |
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: rexeqbidv 2685 rexeqbidva 2687 fnunirn 5767 cbvexfo 5786 fival 6968 nninfwlpoimlemg 7172 nninfwlpoimlemginf 7173 nninfwlpoim 7175 genipv 7507 exfzdc 10237 zproddc 11582 infssuzex 11944 nninfdcex 11948 ennnfonelemrnh 12411 grppropd 12847 dvdsrpropdg 13269 cnpfval 13588 |
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