Metamath Proof Explorer


Theorem rp-8frege

Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019)

Ref Expression
Assertion rp-8frege
|- ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) )

Proof

Step Hyp Ref Expression
1 rp-6frege
 |-  ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )
2 ax-frege2
 |-  ( ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) ) -> ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) ) )
3 1 2 ax-mp
 |-  ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) )