MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  merco1lem15 Unicode version

Theorem merco1lem15 1502
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1484. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem15  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ch 
->  ps ) ) )

Proof of Theorem merco1lem15
StepHypRef Expression
1 merco1lem14 1501 . 2  |-  ( ( ( ( ph  ->  ps )  ->  ps )  ->  ( ch  ->  ps ) )  ->  ( ph  ->  ( ch  ->  ps ) ) )
2 merco1lem13 1500 . 2  |-  ( ( ( ( ( ph  ->  ps )  ->  ps )  ->  ( ch  ->  ps ) )  ->  ( ph  ->  ( ch  ->  ps ) ) )  -> 
( ( ph  ->  ps )  ->  ( ph  ->  ( ch  ->  ps ) ) ) )
31, 2ax-mp 8 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ch 
->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  merco1lem16  1503  retbwax1  1506
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 178  df-tru 1325  df-fal 1326
  Copyright terms: Public domain W3C validator