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Theorem eubid 2302
 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 319 . . . 4
41, 3albid 1885 . . 3
54exbidv 1714 . 2
6 df-eu 2286 . 2
7 df-eu 2286 . 2
85, 6, 73bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616  E!weu 2282 This theorem is referenced by:  mobid  2303  eubidv  2304  euor  2331  euor2  2333  euan  2351  reubida  3040  reueq1f  3052  eusv2i  4649  reusv2lem3  4655  eubi  31343 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617  df-eu 2286
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