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Theorem rabsnt 3445
 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 3402 . . 3
3 id 19 . . 3
42, 3syl5eleqr 2127 . 2
5 rabsnt.2 . . . 4
65elrab 2698 . . 3
76simprbi 260 . 2
84, 7syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  crab 2310  cvv 2557  csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-sn 3381 This theorem is referenced by:  ontr2exmid  4250  onsucsssucexmid  4252  ordsoexmid  4286
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