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Theorem seex 4257
 Description: The -preimage of an element of the base set in a set-like relation is a set. (Contributed by Mario Carneiro, 19-Nov-2014.)
Assertion
Ref Expression
seex Se
Distinct variable groups:   ,   ,   ,

Proof of Theorem seex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-se 4255 . 2 Se
2 breq2 3933 . . . . 5
32rabbidv 2675 . . . 4
43eleq1d 2208 . . 3
54rspccva 2788 . 2
61, 5sylanb 282 1 Se
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wcel 1480  wral 2416  crab 2420  cvv 2686   class class class wbr 3929   Se wse 4251 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 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rab 2425  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-se 4255 This theorem is referenced by:  sefvex  5442
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