![]() |
Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > frege12 | Structured version Visualization version GIF version |
Description: A closed form of com23 86. Proposition 12 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege12 | ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege8 42155 | . 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃))) | |
2 | frege5 42146 | . 2 ⊢ (((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42136 ax-frege2 42137 ax-frege8 42155 |
This theorem is referenced by: frege24 42161 frege16 42162 frege13 42168 frege15 42172 frege35 42184 frege49 42199 frege60a 42224 frege60b 42251 frege60c 42269 frege85 42294 frege127 42336 |
Copyright terms: Public domain | W3C validator |