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Theorem exists2 1876
 Description: A condition implying that at least two things exist. (The proof was 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 hbeu1 1801 . . . . . 6
2 hba1 1441 . . . . . 6
3 exists1 1875 . . . . . . 7
4 ax-16 1606 . . . . . . 7
53, 4sylbi 184 . . . . . 6
61, 2, 5exlimd 1487 . . . . 5
76com12 26 . . . 4
8 alex 1349 . . . 4
97, 8syl6ib 214 . . 3
109con2d 104 . 2
1110imp 412 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 355  wal 1322  wex 1327   wceq 1398  weu 1791 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1323  ax-6 1324  ax-7 1325  ax-gen 1326  ax-8 1402  ax-10 1403  ax-11 1404  ax-12 1405  ax-17 1413  ax-9 1424  ax-4 1429  ax-16 1606 This theorem depends on definitions:  df-bi 174  df-an 357  df-ex 1328  df-eu 1795
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