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Theorem re1tbw2 1501
Description: tbw-ax2 1456 rederived from merco2 1491. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw2  |-  ( ph  ->  ( ps  ->  ph )
)

Proof of Theorem re1tbw2
StepHypRef Expression
1 mercolem1 1492 . . . 4  |-  ( ( ( ph  ->  ph )  ->  ph )  ->  ( ph  ->  ( ps  ->  ph ) ) )
2 mercolem1 1492 . . . 4  |-  ( ( ( ( ph  ->  ph )  ->  ph )  -> 
( ph  ->  ( ps 
->  ph ) ) )  ->  ( ph  ->  ( ps  ->  ( ph  ->  ( ps  ->  ph )
) ) ) )
31, 2ax-mp 8 . . 3  |-  ( ph  ->  ( ps  ->  ( ph  ->  ( ps  ->  ph ) ) ) )
4 mercolem6 1497 . . 3  |-  ( (
ph  ->  ( ps  ->  (
ph  ->  ( ps  ->  ph ) ) ) )  ->  ( ps  ->  (
ph  ->  ( ps  ->  ph ) ) ) )
53, 4ax-mp 8 . 2  |-  ( ps 
->  ( ph  ->  ( ps  ->  ph ) ) )
6 mercolem6 1497 . 2  |-  ( ( ps  ->  ( ph  ->  ( ps  ->  ph )
) )  ->  ( ph  ->  ( ps  ->  ph ) ) )
75, 6ax-mp 8 1  |-  ( ph  ->  ( ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  re1tbw4  1503  ltrneq  30338
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
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