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Theorem 2albidv 1821
Description: Formula-building rule for 2 existential quantifiers (deduction form). (Contributed by NM, 4-Mar-1997.)
Hypothesis
Ref Expression
2albidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
2albidv  |-  ( ph  ->  ( A. x A. y ps  <->  A. x A. y ch ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)    ch( x, y)

Proof of Theorem 2albidv
StepHypRef Expression
1 2albidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21albidv 1778 . 2  |-  ( ph  ->  ( A. y ps  <->  A. y ch ) )
32albidv 1778 1  |-  ( ph  ->  ( A. x A. y ps  <->  A. x A. y ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-17 1489
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  dff13  5635  qliftfun  6477
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