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Theorem sess1 4552
 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 445 . . . . . 6
21ssbrd 4255 . . . . 5
32ss2rabdv 3426 . . . 4
4 ssexg 4351 . . . . 5
54ex 425 . . . 4
63, 5syl 16 . . 3
76ralimdv 2787 . 2
8 df-se 4544 . 2 Se
9 df-se 4544 . 2 Se
107, 8, 93imtr4g 263 1 Se Se
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726  wral 2707  crab 2711  cvv 2958   wss 3322   class class class wbr 4214   Se wse 4541 This theorem is referenced by:  seeq1  4556 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332 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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rab 2716  df-v 2960  df-in 3329  df-ss 3336  df-br 4215  df-se 4544
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