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Theorem eubid 1904
Description: Formula-building rule for uniqueness quantifier (deduction rule). (Contributed by NM, 9-Jul-1994.)
Hypotheses
Ref Expression
eubid.1  F/
eubid.2
Assertion
Ref Expression
eubid

Proof of Theorem eubid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eubid.1 . . . 4  F/
2 eubid.2 . . . . 5
32bibi1d 222 . . . 4
41, 3albid 1503 . . 3
54exbidv 1703 . 2
6 df-eu 1900 . 2
7 df-eu 1900 . 2
85, 6, 73bitr4g 212 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   F/wnf 1346  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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-eu 1900
This theorem is referenced by:  eubidv  1905  mobid  1932  reubida  2485  reueq1f  2497  eusv2i  4153
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