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Theorem rabsnt 3881
 Description: Truth implied by equality of a restricted class abstraction and a singleton. (Contributed by NM, 29-May-2006.) (Proof shortened by Mario Carneiro, 23-Dec-2016.)
Hypotheses
Ref Expression
rabsnt.1
rabsnt.2
Assertion
Ref Expression
rabsnt
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rabsnt
StepHypRef Expression
1 rabsnt.1 . . . 4
21snid 3841 . . 3
3 id 20 . . 3
42, 3syl5eleqr 2523 . 2
5 rabsnt.2 . . . 4
65elrab 3092 . . 3
76simprbi 451 . 2
84, 7syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  crab 2709  cvv 2956  csn 3814 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-sn 3820
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