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Theorem rabsnt 3797
 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 3760 . . 3
3 id 19 . . 3
42, 3syl5eleqr 2440 . 2
5 rabsnt.2 . . . 4
65elrab 2994 . . 3
76simprbi 450 . 2
84, 7syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642   wcel 1710  crab 2618  cvv 2859  csn 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-rab 2623  df-v 2861  df-sn 3741 This theorem is referenced by: (None)
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