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 ) ) ) |
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 ) ) ) |