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Theorem 2exbidv 1796
Description: Formula-building rule for 2 existential quantifiers (deduction form). (Contributed by NM, 1-May-1995.)
Hypothesis
Ref Expression
2albidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
2exbidv  |-  ( ph  ->  ( E. x E. y ps  <->  E. x E. y ch ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)    ch( x, y)

Proof of Theorem 2exbidv
StepHypRef Expression
1 2albidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21exbidv 1753 . 2  |-  ( ph  ->  ( E. y ps  <->  E. y ch ) )
32exbidv 1753 1  |-  ( ph  ->  ( E. x E. y ps  <->  E. x E. y ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   E.wex 1426
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
This theorem is referenced by:  3exbidv  1797  4exbidv  1798  cbvex4v  1853  ceqsex3v  2661  ceqsex4v  2662  copsexg  4071  euotd  4081  elopab  4085  elxpi  4454  relop  4586  cbvoprab3  5724  ov6g  5782  th3qlem1  6392  ltresr  7374  fisumcom2  10828
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