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Theorem eubidv 1956
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 1466 . 2  |-  F/ x ph
2 eubidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2eubid 1955 1  |-  ( ph  ->  ( E! x ps  <->  E! x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   E!weu 1948
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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-eu 1951
This theorem is referenced by:  eubii  1957  eueq2dc  2788  eueq3dc  2789  reuhypd  4293  feu  5193  funfveu  5318  dff4im  5445  acexmid  5651
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