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Theorem exists2 1994
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 1907 . . . . . 6
2 hba1 1430 . . . . . 6
3 exists1 1993 . . . . . . 7
4 ax16 1691 . . . . . . 7
53, 4sylbi 114 . . . . . 6
61, 2, 5exlimdh 1484 . . . . 5
76com12 27 . . . 4
8 alexim 1533 . . . 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 1240   wceq 1242  wex 1378  weu 1897
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-eu 1900
This theorem is referenced by: (None)
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