Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-ax12wlem Structured version   Unicode version

Theorem bj-ax12wlem 31007
Description: The general statement that ax12wlem 1880 proves. (Contributed by BJ, 20-Mar-2020.)
Hypothesis
Ref Expression
bj-ax12wlem.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
bj-ax12wlem  |-  ( ph  ->  ( ps  ->  A. x
( ph  ->  ps )
) )
Distinct variable group:    ch, x
Allowed substitution hints:    ph( x)    ps( x)

Proof of Theorem bj-ax12wlem
StepHypRef Expression
1 bj-ax12wlem.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
2 ax-5 1751 . 2  |-  ( ch 
->  A. x ch )
31, 2bj-ax12i 31005 1  |-  ( ph  ->  ( ps  ->  A. x
( ph  ->  ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751
This theorem depends on definitions:  df-bi 188
This theorem is referenced by:  bj-ax12w  31016
  Copyright terms: Public domain W3C validator