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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege7 | Structured version Visualization version GIF version |
Description: A closed form of syl6 35. The first antecedent is used to replace the consequent of the second antecedent. Proposition 7 of [Frege1879] p. 34. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege7 | ⊢ ((𝜑 → 𝜓) → ((𝜒 → (𝜃 → 𝜑)) → (𝜒 → (𝜃 → 𝜓)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege5 40153 | . 2 ⊢ ((𝜑 → 𝜓) → ((𝜃 → 𝜑) → (𝜃 → 𝜓))) | |
2 | frege6 40159 | . 2 ⊢ (((𝜑 → 𝜓) → ((𝜃 → 𝜑) → (𝜃 → 𝜓))) → ((𝜑 → 𝜓) → ((𝜒 → (𝜃 → 𝜑)) → (𝜒 → (𝜃 → 𝜓))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → (𝜃 → 𝜑)) → (𝜒 → (𝜃 → 𝜓)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 40143 ax-frege2 40144 |
This theorem is referenced by: frege32 40188 frege67a 40238 frege67b 40265 frege67c 40283 frege94 40310 frege107 40323 frege113 40329 |
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