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Theorem exists2 2294
 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 2214 . . . . . 6
2 nfa1 1788 . . . . . 6
3 exists1 2293 . . . . . . 7
4 ax16 2045 . . . . . . 7
53, 4sylbi 187 . . . . . 6
61, 2, 5exlimd 1806 . . . . 5
76com12 27 . . . 4
8 alex 1572 . . . 4
97, 8syl6ib 217 . . 3
109con2d 107 . 2
1110imp 418 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541   wceq 1642  weu 2204 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  df-eu 2208 This theorem is referenced by: (None)
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