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Theorem rexsns 3847
 Description: Restricted existential quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.)
Assertion
Ref Expression
rexsns
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rexsns
StepHypRef Expression
1 sbc5 3187 . . 3
21a1i 11 . 2
3 df-rex 2713 . . 3
4 elsn 3831 . . . . 5
54anbi1i 678 . . . 4
65exbii 1593 . . 3
73, 6bitri 242 . 2
82, 7syl6rbbr 257 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  wrex 2708  wsbc 3163  csn 3816 This theorem is referenced by:  rexsng  3849  r19.12sn  3874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960  df-sbc 3164  df-sn 3822
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