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Theorem exists2 1997
 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 hbeu1 1910 . . . . . 6
2 hba1 1433 . . . . . 6
3 exists1 1996 . . . . . . 7
4 ax16 1694 . . . . . . 7
53, 4sylbi 114 . . . . . 6
61, 2, 5exlimdh 1487 . . . . 5
76com12 27 . . . 4
8 alexim 1536 . . . 4
97, 8syl6 29 . . 3
109con2d 554 . 2
1110imp 115 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97  wal 1241   wceq 1243  wex 1381  weu 1900 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-eu 1903 This theorem is referenced by: (None)
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