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Theorem rexsns 3409
 Description: Restricted existential quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.) (Revised by NM, 22-Aug-2018.)
Assertion
Ref Expression
rexsns
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rexsns
StepHypRef Expression
1 velsn 3392 . . . 4
21anbi1i 431 . . 3
32exbii 1496 . 2
4 df-rex 2312 . 2
5 sbc5 2787 . 2
63, 4, 53bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wceq 1243  wex 1381   wcel 1393  wrex 2307  wsbc 2764  csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-sn 3381 This theorem is referenced by: (None)
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