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Theorem exists2 1754
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 1679 . . . . . 6
2 hba1 1299 . . . . . 6
3 exists1 1753 . . . . . . 7
4 ax-16 1481 . . . . . . 7
53, 4sylbi 112 . . . . . 6
61, 2, 5exlimd 1333 . . . . 5
76com12 25 . . . 4
8 alex 1663 . . . 4
97, 8syl6ib 148 . . 3
109con2d 535 . 2
1110imp 113 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 95  wal 1214  wex 1253   wceq 1262  weu 1669
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in1 526  ax-in2 527  ax-io 606  ax-3 714  ax-5 1215  ax-7 1217  ax-gen 1218  ax-ie1 1254  ax-ie2 1255  ax-8 1266  ax-10 1267  ax-11 1268  ax-i12 1270  ax-4 1271  ax-17 1280  ax-i9 1282  ax-ial 1293  ax-16 1481
This theorem depends on definitions:  df-bi 108  df-tru 1192  df-fal 1193  df-eu 1673
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