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Theorem rabsssn 4002
 Description: Conditions for a restricted class abstraction to be a subset of a singleton, i.e. to be a singleton or the empty set. (Contributed by AV, 18-Apr-2019.)
Assertion
Ref Expression
rabsssn
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rabsssn
StepHypRef Expression
1 df-rab 2746 . . 3
2 df-sn 3969 . . 3
31, 2sseq12i 3458 . 2
4 ss2ab 3497 . 2
5 impexp 448 . . . 4
65albii 1691 . . 3
7 df-ral 2742 . . 3
86, 7bitr4i 256 . 2
93, 4, 83bitri 275 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442   wceq 1444   wcel 1887  cab 2437  wral 2737  crab 2741   wss 3404  csn 3968 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rab 2746  df-in 3411  df-ss 3418  df-sn 3969 This theorem is referenced by:  suppmptcfin  40217  linc1  40271
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