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Theorem reubidv 2550
Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 17-Oct-1996.)
Hypothesis
Ref Expression
reubidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
reubidv  |-  ( ph  ->  ( E! x  e.  A  ps  <->  E! x  e.  A  ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem reubidv
StepHypRef Expression
1 reubidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21adantr 270 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
32reubidva 2549 1  |-  ( ph  ->  ( E! x  e.  A  ps  <->  E! x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    e. wcel 1438   E!wreu 2361
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  df-reu 2366
This theorem is referenced by:  reueqd  2572  sbcreug  2919  xpf1o  6560  srpospr  7328  creur  8419  creui  8420  divalg2  11204
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