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Theorem reuhyp 4204
 Description: A theorem useful for eliminating restricted existential uniqueness hypotheses. (Contributed by NM, 15-Nov-2004.)
Hypotheses
Ref Expression
reuhyp.1
reuhyp.2
Assertion
Ref Expression
reuhyp
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem reuhyp
StepHypRef Expression
1 tru 1247 . 2
2 reuhyp.1 . . . 4
32adantl 262 . . 3
4 reuhyp.2 . . . 4
543adant1 922 . . 3
63, 5reuhypd 4203 . 2
71, 6mpan 400 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   wtru 1244   wcel 1393  wreu 2308 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-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-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-reu 2313  df-v 2559 This theorem is referenced by: (None)
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