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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege50 | Structured version Visualization version GIF version |
Description: Closed form of jaoi 856. Proposition 50 of [Frege1879] p. 49. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege50 | ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((¬ 𝜑 → 𝜒) → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege49 42030 | . 2 ⊢ ((¬ 𝜑 → 𝜒) → ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → 𝜓))) | |
2 | frege17 41998 | . 2 ⊢ (((¬ 𝜑 → 𝜒) → ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → 𝜓))) → ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((¬ 𝜑 → 𝜒) → 𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((¬ 𝜑 → 𝜒) → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 41967 ax-frege2 41968 ax-frege8 41986 ax-frege28 42007 ax-frege31 42011 ax-frege41 42022 |
This theorem is referenced by: frege51 42032 |
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