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Theorem reubii 2555
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 2554 1  |-  ( E! x  e.  A  ph  <->  E! x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    e. wcel 1439   E!wreu 2362
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-eu 1952  df-reu 2367
This theorem is referenced by:  caucvgsrlemcl  7397  axcaucvglemcl  7493  axcaucvglemval  7495
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