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Theorem eubii 1951
Description: Introduce uniqueness quantifier to both sides of an equivalence. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
eubii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
eubii  |-  ( E! x ph  <->  E! x ps )

Proof of Theorem eubii
StepHypRef Expression
1 eubii.1 . . . 4  |-  ( ph  <->  ps )
21a1i 9 . . 3  |-  ( T. 
->  ( ph  <->  ps )
)
32eubidv 1950 . 2  |-  ( T. 
->  ( E! x ph  <->  E! x ps ) )
43trud 1294 1  |-  ( E! x ph  <->  E! x ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   T. wtru 1286   E!weu 1942
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-eu 1945
This theorem is referenced by:  cbveu  1966  2eu7  2036  reubiia  2539  cbvreu  2576  reuv  2619  euxfr2dc  2778  euxfrdc  2779  2reuswapdc  2795  reuun2  3254  zfnuleu  3910  copsexg  4007  funeu2  4957  funcnv3  4992  fneu2  5035  tz6.12  5233  f1ompt  5352  fsn  5367  climreu  10274  divalgb  10469
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