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Theorem 2exsb 2132
 Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.)
Assertion
Ref Expression
2exsb
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem 2exsb
StepHypRef Expression
1 exsb 2130 . . . 4
21exbii 1582 . . 3
3 excom 1741 . . 3
42, 3bitri 240 . 2
5 exsb 2130 . . . . 5
6 impexp 433 . . . . . . . . 9
76albii 1566 . . . . . . . 8
8 19.21v 1890 . . . . . . . 8
97, 8bitr2i 241 . . . . . . 7
109albii 1566 . . . . . 6
1110exbii 1582 . . . . 5
125, 11bitri 240 . . . 4
1312exbii 1582 . . 3
14 excom 1741 . . 3
1513, 14bitri 240 . 2
164, 15bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541 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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  2eu6  2289
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