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Theorem eubidv 2027
Description: Formula-building rule for unique existential quantifier (deduction form). (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 1521 . 2  |-  F/ x ph
2 eubidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2eubid 2026 1  |-  ( ph  ->  ( E! x ps  <->  E! x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   E!weu 2019
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022
This theorem is referenced by:  eubii  2028  eueq2dc  2903  eueq3dc  2904  reuhypd  4454  feu  5378  funfveu  5507  dff4im  5640  acexmid  5850  upxp  13027  dedekindicc  13366
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