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Metamath Proof Explorer

Theorem re1tbw2

Description: tbw-ax2 rederived from merco2 . (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion re1tbw2 
|- ( ph -> ( ps -> ph ) )

Proof

Step Hyp Ref Expression
1 mercolem1 
 |-  ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) )
2 mercolem1 
 |-  ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) )
3 1 2 ax-mp 
 |-  ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
4 mercolem6 
 |-  ( ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
5 3 4 ax-mp 
 |-  ( ps -> ( ph -> ( ps -> ph ) ) )
6 mercolem6 
 |-  ( ( ps -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ph ) ) )
7 5 6 ax-mp 
 |-  ( ph -> ( ps -> ph ) )