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Theorem 2exsb 2213
Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Wolf Lammen, 30-Sep-2018.)
Assertion
Ref Expression
2exsb
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem 2exsb
StepHypRef Expression
1 2sb8e 2211 . 2
2 2sb6 2188 . . 3
322exbii 1668 . 2
41, 3bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  [wsb 1739
This theorem is referenced by:  2moOLD  2374  2eu6  2383  2eu6OLD  2384
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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