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Theorem merco1lem8 1479
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1468. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem8  |-  ( ph  ->  ( ( ps  ->  ( ps  ->  ch )
)  ->  ( ps  ->  ch ) ) )

Proof of Theorem merco1lem8
StepHypRef Expression
1 merco1lem6 1476 . 2  |-  ( ( ps  ->  ( ps  ->  ch ) )  -> 
( ( ps  ->  ( ps  ->  ch )
)  ->  ( ps  ->  ch ) ) )
2 merco1lem6 1476 . 2  |-  ( ( ( ps  ->  ( ps  ->  ch ) )  ->  ( ( ps 
->  ( ps  ->  ch ) )  ->  ( ps  ->  ch ) ) )  ->  ( ph  ->  ( ( ps  ->  ( ps  ->  ch )
)  ->  ( ps  ->  ch ) ) ) )
31, 2ax-mp 8 1  |-  ( ph  ->  ( ( ps  ->  ( ps  ->  ch )
)  ->  ( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  merco1lem9  1480  merco1lem14  1485
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