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Theorem rp-6frege 38097
Description: Elimination of a nested antecedent of special form. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
rp-6frege |- ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )
Proof of Theorem rp-6frege
StepHypRef Expression
1 rp-4frege 38096 . 2 |- ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) )
2 ax-frege1 38084 . 2 |- ( ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) -> ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) ) )
31, 2ax-mp 5 1 |- ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )
Colors of variables: wff setvar class
Syntax hints:   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085
This theorem is referenced by:  rp-8frege  38098
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