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Theorem 2exbidv 1791
Description: Formula-building rule for 2 existential quantifiers (deduction rule). (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 1748 . 2  |-  ( ph  ->  ( E. y ps  <->  E. y ch ) )
32exbidv 1748 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 1422
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
This theorem is referenced by:  3exbidv  1792  4exbidv  1793  cbvex4v  1848  ceqsex3v  2650  ceqsex4v  2651  copsexg  4027  euotd  4037  elopab  4041  elxpi  4407  relop  4534  cbvoprab3  5631  ov6g  5689  th3qlem1  6295  ltresr  7121
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