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Theorem 2exsbOLD7 29767
 Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.)
Assertion
Ref Expression
2exsbOLD7
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem 2exsbOLD7
StepHypRef Expression
1 exsbNEW7 29599 . . . 4
21exbii 1592 . . 3
3 excomOLD7 29694 . . 3
42, 3bitri 241 . 2
5 exsbNEW7 29599 . . . . 5
6 impexp 434 . . . . . . . . 9
76albii 1575 . . . . . . . 8
8 19.21v 1913 . . . . . . . 8
97, 8bitr2i 242 . . . . . . 7
109albii 1575 . . . . . 6
1110exbii 1592 . . . . 5
125, 11bitri 241 . . . 4
1312exbii 1592 . . 3
14 excomOLD7 29694 . . 3
1513, 14bitri 241 . 2
164, 15bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950  ax-7v 29442  ax-7OLD7 29678 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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