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Theorem exse 4291
 Description: Any relation on a set is set-like on it. (Contributed by Mario Carneiro, 22-Jun-2015.)
Assertion
Ref Expression
exse Se

Proof of Theorem exse
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rabexg 4103 . . 3
21ralrimivw 2528 . 2
3 df-se 4288 . 2 Se
42, 3sylibr 133 1 Se
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 2125  wral 2432  crab 2436  cvv 2709   class class class wbr 3961   Se wse 4284 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136  ax-sep 4078 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rab 2441  df-v 2711  df-in 3104  df-ss 3111  df-se 4288 This theorem is referenced by: (None)
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