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Theorem wl-alanbii 30261
Description: This theorem extends alanimi 1642 to a biconditional. Recurrent usage stacks up more quantifiers. (Contributed by Wolf Lammen, 4-Oct-2019.)
Hypothesis
Ref Expression
wl-alanbii.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
wl-alanbii  |-  ( A. x ph  <->  ( A. x ps  /\  A. x ch ) )

Proof of Theorem wl-alanbii
StepHypRef Expression
1 wl-alanbii.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
21albii 1645 . 2  |-  ( A. x ph  <->  A. x ( ps 
/\  ch ) )
3 19.26 1685 . 2  |-  ( A. x ( ps  /\  ch )  <->  ( A. x ps  /\  A. x ch ) )
42, 3bitri 249 1  |-  ( A. x ph  <->  ( A. x ps  /\  A. x ch ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-an 369
This theorem is referenced by: (None)
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