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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege14 | Structured version Visualization version GIF version |
Description: Closed form of a deduction based on com3r 87. Proposition 14 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege14 | ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege13 42182 | . 2 ⊢ ((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜃 → (𝜓 → (𝜒 → 𝜏)))) | |
2 | frege5 42160 | . 2 ⊢ (((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜃 → (𝜓 → (𝜒 → 𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏)))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏))))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42150 ax-frege2 42151 ax-frege8 42169 |
This theorem is referenced by: frege15 42186 |
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