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Theorem merco1lem16 1487
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1468. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem16  |-  ( ( ( ph  ->  ( ps  ->  ch ) )  ->  ta )  -> 
( ( ph  ->  ch )  ->  ta )
)

Proof of Theorem merco1lem16
StepHypRef Expression
1 merco1lem15 1486 . . 3  |-  ( (
ph  ->  ch )  -> 
( ph  ->  ( ps 
->  ch ) ) )
2 merco1lem11 1482 . . 3  |-  ( ( ( ph  ->  ch )  ->  ( ph  ->  ( ps  ->  ch )
) )  ->  (
( ( ( ta 
->  ph )  ->  (
( ph  ->  ch )  ->  F.  ) )  ->  F.  )  ->  ( ph  ->  ( ps  ->  ch ) ) ) )
31, 2ax-mp 8 . 2  |-  ( ( ( ( ta  ->  ph )  ->  ( ( ph  ->  ch )  ->  F.  ) )  ->  F.  )  ->  ( ph  ->  ( ps  ->  ch )
) )
4 merco1 1468 . 2  |-  ( ( ( ( ( ta 
->  ph )  ->  (
( ph  ->  ch )  ->  F.  ) )  ->  F.  )  ->  ( ph  ->  ( ps  ->  ch ) ) )  -> 
( ( ( ph  ->  ( ps  ->  ch ) )  ->  ta )  ->  ( ( ph  ->  ch )  ->  ta ) ) )
53, 4ax-mp 8 1  |-  ( ( ( ph  ->  ( ps  ->  ch ) )  ->  ta )  -> 
( ( ph  ->  ch )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1308
This theorem is referenced by:  merco1lem17  1488  retbwax1  1490
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-fal 1311
  Copyright terms: Public domain W3C validator