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Theorem eubid 1950
 Description: Formula-building rule for uniqueness quantifier (deduction rule). (Contributed by NM, 9-Jul-1994.)
Hypotheses
Ref Expression
eubid.1
eubid.2
Assertion
Ref Expression
eubid

Proof of Theorem eubid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eubid.1 . . . 4
2 eubid.2 . . . . 5
32bibi1d 231 . . . 4
41, 3albid 1547 . . 3
54exbidv 1748 . 2
6 df-eu 1946 . 2
7 df-eu 1946 . 2
85, 6, 73bitr4g 221 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283  wnf 1390  wex 1422  weu 1943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-eu 1946 This theorem is referenced by:  eubidv  1951  mobid  1978  reubida  2540  reueq1f  2552  eusv2i  4233
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