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Theorem sess1 4266
 Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.)
Assertion
Ref Expression
sess1 Se Se

Proof of Theorem sess1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simpl 108 . . . . . 6
21ssbrd 3978 . . . . 5
32ss2rabdv 3182 . . . 4
4 ssexg 4074 . . . . 5
54ex 114 . . . 4
63, 5syl 14 . . 3
76ralimdv 2503 . 2
8 df-se 4262 . 2 Se
9 df-se 4262 . 2 Se
107, 8, 93imtr4g 204 1 Se Se
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 1481  wral 2417  crab 2421  cvv 2689   wss 3075   class class class wbr 3936   Se wse 4258 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rab 2426  df-v 2691  df-in 3081  df-ss 3088  df-br 3937  df-se 4262 This theorem is referenced by:  seeq1  4268
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