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Theorem exsb 2212
Description: An equivalent expression for existence. (Contributed by NM, 2-Feb-2005.)
Assertion
Ref Expression
exsb
Distinct variable groups:   ,   ,

Proof of Theorem exsb
StepHypRef Expression
1 nfv 1707 . 2
2 nfa1 1897 . 2
3 ax12v 1855 . . 3
4 sp 1859 . . . 4
54com12 31 . . 3
63, 5impbid 191 . 2
71, 2, 6cbvex 2022 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612
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
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