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Theorem sess2 4580
 Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.)
Assertion
Ref Expression
sess2 Se Se

Proof of Theorem sess2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssralv 3393 . . 3
2 rabss2 3412 . . . . 5
3 ssexg 4378 . . . . . 6
43ex 425 . . . . 5
52, 4syl 16 . . . 4
65ralimdv 2791 . . 3
71, 6syld 43 . 2
8 df-se 4571 . 2 Se
9 df-se 4571 . 2 Se
107, 8, 93imtr4g 263 1 Se Se
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1727  wral 2711  crab 2715  cvv 2962   wss 3306   class class class wbr 4237   Se wse 4568 This theorem is referenced by:  seeq2  4584  wereu2  4608  frmin  25548  wfrlem5  25573  frrlem5  25617 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rab 2720  df-v 2964  df-in 3313  df-ss 3320  df-se 4571
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