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Theorem elex2 2871
 Description: If a class contains another class, then it contains some set. (Contributed by Alan Sare, 25-Sep-2011.)
Assertion
Ref Expression
elex2 (A Bx x B)
Distinct variable groups:   x,A   x,B

Proof of Theorem elex2
StepHypRef Expression
1 eleq1a 2422 . . 3 (A B → (x = Ax B))
21alrimiv 1631 . 2 (A Bx(x = Ax B))
3 elisset 2869 . 2 (A Bx x = A)
4 exim 1575 . 2 (x(x = Ax B) → (x x = Ax x B))
52, 3, 4sylc 56 1 (A Bx x B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1541   = wceq 1642   ∈ wcel 1710 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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