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Theorem 2sb8e 2211
Description: An equivalent expression for double existence. (Contributed by Wolf Lammen, 2-Nov-2019.)
Assertion
Ref Expression
2sb8e
Distinct variable group:   , ,

Proof of Theorem 2sb8e
StepHypRef Expression
1 nfv 1707 . . . . 5
21sb8e 2168 . . . 4
32exbii 1667 . . 3
4 excom 1849 . . 3
53, 4bitri 249 . 2
6 nfv 1707 . . . . 5
76nfsb 2184 . . . 4
87sb8e 2168 . . 3
98exbii 1667 . 2
10 excom 1849 . 2
115, 9, 103bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  E.wex 1612  [wsb 1739
This theorem is referenced by:  2exsb  2213  2mo  2373
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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