Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > frege15 | Structured version Visualization version GIF version |
Description: A closed form of com4r 94. Proposition 15 of [Frege1879] p. 38. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege15 | ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒 → 𝜏))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege14 41401 | . 2 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏))))) | |
2 | frege12 41391 | . 2 ⊢ (((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏))))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒 → 𝜏)))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒 → 𝜏))))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 41368 ax-frege2 41369 ax-frege8 41387 |
This theorem is referenced by: frege88 41529 |
Copyright terms: Public domain | W3C validator |