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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege51 | Structured version Visualization version GIF version |
Description: Compare with jaod 859. Proposition 51 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege51 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜒) → (𝜑 → ((¬ 𝜓 → 𝜃) → 𝜒)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege50 41139 | . 2 ⊢ ((𝜓 → 𝜒) → ((𝜃 → 𝜒) → ((¬ 𝜓 → 𝜃) → 𝜒))) | |
2 | frege18 41103 | . 2 ⊢ (((𝜓 → 𝜒) → ((𝜃 → 𝜒) → ((¬ 𝜓 → 𝜃) → 𝜒))) → ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜒) → (𝜑 → ((¬ 𝜓 → 𝜃) → 𝜒))))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜒) → (𝜑 → ((¬ 𝜓 → 𝜃) → 𝜒)))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 41075 ax-frege2 41076 ax-frege8 41094 ax-frege28 41115 ax-frege31 41119 ax-frege41 41130 |
This theorem is referenced by: frege128 41276 |
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