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Theorem exists2 2389
Description: A condition implying that at least two things exist. (Contributed by NM, 10-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
exists2

Proof of Theorem exists2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfeu1 2294 . . . . . 6
2 nfa1 1897 . . . . . 6
3 exists1 2388 . . . . . . 7
4 axc16 1941 . . . . . . 7
53, 4sylbi 195 . . . . . 6
61, 2, 5exlimd 1914 . . . . 5
76com12 31 . . . 4
8 alex 1647 . . . 4
97, 8syl6ib 226 . . 3
109con2d 115 . 2
1110imp 429 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282
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-eu 2286
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