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Theorem elex22 3122
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 2540 . . . 4
2 eleq1a 2540 . . . 4
31, 2anim12ii 570 . . 3
43alrimiv 1719 . 2
5 elisset 3120 . . 3
65adantr 465 . 2
7 exim 1654 . 2
84, 6, 7sylc 60 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818
This theorem is referenced by:  en3lplem1VD  33643
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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