Description: A single axiom for propositional calculus discovered by C. A. Meredith.
This axiom is worthy of note, due to it having only 19 symbols, not counting parentheses. The more well-known meredith has 21 symbols, sans parentheses.
See merco2 for another axiom of equal length. (Contributed by Anthony Hart, 13-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | merco1 | |- ( ( ( ( ( ph -> ps ) -> ( ch -> F. ) ) -> th ) -> ta ) -> ( ( ta -> ph ) -> ( ch -> ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-1 | |- ( -. ch -> ( -. th -> -. ch ) ) |
|
| 2 | falim | |- ( F. -> ( -. th -> -. ch ) ) |
|
| 3 | 1 2 | ja | |- ( ( ch -> F. ) -> ( -. th -> -. ch ) ) |
| 4 | 3 | imim2i | |- ( ( ( ph -> ps ) -> ( ch -> F. ) ) -> ( ( ph -> ps ) -> ( -. th -> -. ch ) ) ) |
| 5 | 4 | imim1i | |- ( ( ( ( ph -> ps ) -> ( -. th -> -. ch ) ) -> th ) -> ( ( ( ph -> ps ) -> ( ch -> F. ) ) -> th ) ) |
| 6 | 5 | imim1i | |- ( ( ( ( ( ph -> ps ) -> ( ch -> F. ) ) -> th ) -> ta ) -> ( ( ( ( ph -> ps ) -> ( -. th -> -. ch ) ) -> th ) -> ta ) ) |
| 7 | meredith | |- ( ( ( ( ( ph -> ps ) -> ( -. th -> -. ch ) ) -> th ) -> ta ) -> ( ( ta -> ph ) -> ( ch -> ph ) ) ) |
|
| 8 | 6 7 | syl | |- ( ( ( ( ( ph -> ps ) -> ( ch -> F. ) ) -> th ) -> ta ) -> ( ( ta -> ph ) -> ( ch -> ph ) ) ) |