Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 18-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | merco1lem9 | |- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | merco1lem8 | |- ( ( F. -> ph ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) ) |
|
| 2 | merco1lem8 | |- ( ( ( F. -> ph ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) |