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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege18 | Structured version Visualization version GIF version |
Description: Closed form of a syllogism followed by a swap of antecedents. Proposition 18 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege18 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜑) → (𝜓 → (𝜃 → 𝜒)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege5 43790 | . 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜑) → (𝜃 → (𝜓 → 𝜒)))) | |
2 | frege16 43806 | . 2 ⊢ (((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜑) → (𝜃 → (𝜓 → 𝜒)))) → ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜑) → (𝜓 → (𝜃 → 𝜒))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜑) → (𝜓 → (𝜃 → 𝜒)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 43780 ax-frege2 43781 ax-frege8 43799 |
This theorem is referenced by: frege19 43814 frege23 43815 frege20 43818 frege51 43845 frege64a 43872 frege64b 43899 frege64c 43917 frege82 43935 |
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