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Theorem merco1lem5 1495
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1488. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem5  |-  ( ( ( ( ph  ->  F.  )  ->  ch )  ->  ta )  ->  ( ph  ->  ta ) )

Proof of Theorem merco1lem5
StepHypRef Expression
1 merco1lem4 1494 . 2  |-  ( ( ( ( ta  ->  ph )  ->  ( ph  ->  F.  ) )  ->  ch )  ->  ( (
ph  ->  F.  )  ->  ch ) )
2 merco1 1488 . 2  |-  ( ( ( ( ( ta 
->  ph )  ->  ( ph  ->  F.  ) )  ->  ch )  ->  (
( ph  ->  F.  )  ->  ch ) )  -> 
( ( ( (
ph  ->  F.  )  ->  ch )  ->  ta )  ->  ( ph  ->  ta ) ) )
31, 2ax-mp 5 1  |-  ( ( ( ( ph  ->  F.  )  ->  ch )  ->  ta )  ->  ( ph  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1327
This theorem is referenced by:  merco1lem6  1496  merco1lem7  1497  merco1lem11  1502  merco1lem18  1509
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-tru 1329  df-fal 1330
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