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Theorem sess2 4808
 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 3479 . . 3
2 rabss2 3498 . . . . 5
3 ssexg 4542 . . . . . 6
43ex 441 . . . . 5
52, 4syl 17 . . . 4
65ralimdv 2806 . . 3
71, 6syld 44 . 2
8 df-se 4799 . 2 Se
9 df-se 4799 . 2 Se
107, 8, 93imtr4g 278 1 Se Se
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1904  wral 2756  crab 2760  cvv 3031   wss 3390   class class class wbr 4395   Se wse 4796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rab 2765  df-v 3033  df-in 3397  df-ss 3404  df-se 4799 This theorem is referenced by:  seeq2  4812  wereu2  4836  wfrlem5  7058  frmin  30551  frrlem5  30589
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