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Theorem re1tbw3 1672
Description: tbw-ax3 1627 rederived from merco2 1661. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw3  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )

Proof of Theorem re1tbw3
StepHypRef Expression
1 mercolem2 1663 . 2  |-  ( ( ( ph  ->  ph )  ->  ph )  ->  ( ph  ->  ( ph  ->  ph ) ) )
2 mercolem2 1663 . . 3  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  (
( ( ( ph  ->  ph )  ->  ph )  ->  ( ph  ->  ( ph  ->  ph ) ) )  ->  ( ( (
ph  ->  ps )  ->  ph )  ->  ph )
) )
3 mercolem6 1667 . . 3  |-  ( ( ( ( ph  ->  ps )  ->  ph )  -> 
( ( ( (
ph  ->  ph )  ->  ph )  ->  ( ph  ->  ( ph  ->  ph ) ) )  ->  ( ( (
ph  ->  ps )  ->  ph )  ->  ph )
) )  ->  (
( ( ( ph  ->  ph )  ->  ph )  ->  ( ph  ->  ( ph  ->  ph ) ) )  ->  ( ( (
ph  ->  ps )  ->  ph )  ->  ph )
) )
42, 3ax-mp 5 . 2  |-  ( ( ( ( ph  ->  ph )  ->  ph )  -> 
( ph  ->  ( ph  ->  ph ) ) )  ->  ( ( (
ph  ->  ps )  ->  ph )  ->  ph )
)
51, 4ax-mp 5 1  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
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 197  df-tru 1486  df-fal 1489
This theorem is referenced by:  re1tbw4  1673
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