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Theorem reubii 2616
Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 22-Oct-1999.)
Hypothesis
Ref Expression
reubii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
reubii  |-  ( E! x  e.  A  ph  <->  E! x  e.  A  ps )

Proof of Theorem reubii
StepHypRef Expression
1 reubii.1 . . 3  |-  ( ph  <->  ps )
21a1i 9 . 2  |-  ( x  e.  A  ->  ( ph 
<->  ps ) )
32reubiia 2615 1  |-  ( E! x  e.  A  ph  <->  E! x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    e. wcel 1480   E!wreu 2418
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-eu 2002  df-reu 2423
This theorem is referenced by:  caucvgsrlemcl  7609  axcaucvglemcl  7715  axcaucvglemval  7717
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