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Theorem 2albii 1406
Description: Inference adding 2 universal quantifiers to both sides of an equivalence. (Contributed by NM, 9-Mar-1997.)
Hypothesis
Ref Expression
albii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
2albii  |-  ( A. x A. y ph  <->  A. x A. y ps )

Proof of Theorem 2albii
StepHypRef Expression
1 albii.1 . . 3  |-  ( ph  <->  ps )
21albii 1405 . 2  |-  ( A. y ph  <->  A. y ps )
32albii 1405 1  |-  ( A. x A. y ph  <->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   A.wal 1288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mor  1991  mo4f  2009  moanim  2023  2eu4  2042  ralcomf  2529  raliunxp  4590  cnvsym  4828  intasym  4829  intirr  4831  codir  4833  qfto  4834  dffun4  5039  dffun4f  5044  funcnveq  5090  fun11  5094  fununi  5095  mpt22eqb  5768  addnq0mo  7067  mulnq0mo  7068  addsrmo  7350  mulsrmo  7351
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