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Theorem eubidv 1950
Description: Formula-building rule for uniqueness quantifier (deduction rule). (Contributed by NM, 9-Jul-1994.)
Hypothesis
Ref Expression
eubidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
eubidv  |-  ( ph  ->  ( E! x ps  <->  E! x ch ) )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem eubidv
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
2 eubidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2eubid 1949 1  |-  ( ph  ->  ( E! x ps  <->  E! x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   E!weu 1942
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 1945
This theorem is referenced by:  eubii  1951  eueq2dc  2766  eueq3dc  2767  reuhypd  4229  feu  5103  funfveu  5219  dff4im  5345  acexmid  5542
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