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Theorem rabsnt 3593
 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 3551 . . 3
3 id 19 . . 3
42, 3eleqtrrid 2227 . 2
5 rabsnt.2 . . . 4
65elrab 2835 . . 3
76simprbi 273 . 2
84, 7syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331   wcel 1480  crab 2418  cvv 2681  csn 3522 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rab 2423  df-v 2683  df-sn 3528 This theorem is referenced by:  ontr2exmid  4435  onsucsssucexmid  4437  ordsoexmid  4472  unfiexmid  6799
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