Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-alanbii Structured version   Unicode version

Theorem wl-alanbii 28529
Description: This theorem extends alanimi 1608 to a bi-conditional. 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 1611 . 2  |-  ( A. x ph  <->  A. x ( ps 
/\  ch ) )
3 19.26 1648 . 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 369   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator