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Theorem exsb 2130
Description: An equivalent expression for existence. (Contributed by NM, 2-Feb-2005.)
Assertion
Ref Expression
exsb
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem exsb
StepHypRef Expression
1 nfv 1619 . 2  F/
2 nfa1 1788 . 2  F/
3 ax11v 2096 . . 3
4 sp 1747 . . . 4
54com12 27 . . 3
63, 5impbid 183 . 2
71, 2, 6cbvex 1985 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176  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:  2exsb  2132
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