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Theorem rexsns 3764
 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 3070 . . 3
21a1i 10 . 2
3 df-rex 2620 . . 3
4 elsn 3748 . . . . 5
54anbi1i 676 . . . 4
65exbii 1582 . . 3
73, 6bitri 240 . 2
82, 7syl6rbbr 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615  wsbc 3046  csn 3737 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861  df-sbc 3047  df-sn 3741 This theorem is referenced by:  rexsng  3766  r19.12sn  3789
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