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Theorem 2rexbii 2724
Description: Inference adding two restricted existential quantifiers to both sides of an equivalence. (Contributed by NM, 11-Nov-1995.)
Hypothesis
Ref Expression
ralbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
2rexbii  |-  ( E. x  e.  A  E. y  e.  B  ph  <->  E. x  e.  A  E. y  e.  B  ps )

Proof of Theorem 2rexbii
StepHypRef Expression
1 ralbii.1 . . 3  |-  ( ph  <->  ps )
21rexbii 2722 . 2  |-  ( E. y  e.  B  ph  <->  E. y  e.  B  ps )
32rexbii 2722 1  |-  ( E. x  e.  A  E. y  e.  B  ph  <->  E. x  e.  A  E. y  e.  B  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   E.wrex 2698
This theorem is referenced by:  3reeanv  2868  addcompr  8888  mulcompr  8890  4fvwrd4  11111  pythagtriplem2  13181  pythagtrip  13198  efgrelexlemb  15372  ordthaus  17438  regr1lem2  17762  fmucndlem  18311  xrofsup  24116  ntrivcvgmul  25220  prodmo  25252  poseq  25513  altopelaltxp  25786  axpasch  25845  axeuclid  25867  axcontlem4  25871  brsegle  26007  mzpcompact2lem  26762  7rexfrabdioph  26814  expdiophlem1  27046  frgrawopreglem5  28338
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-rex 2703
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