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Theorem elex22 2870
Description: If two classes each contain another class, then both contain some set. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
elex22
Distinct variable groups:   ,   ,   ,

Proof of Theorem elex22
StepHypRef Expression
1 eleq1a 2422 . . . 4
2 eleq1a 2422 . . . 4
31, 2anim12ii 553 . . 3
43alrimiv 1631 . 2
5 elisset 2869 . . 3
65adantr 451 . 2
7 exim 1575 . 2
84, 6, 7sylc 56 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  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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