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Mirrors > Home > ILE Home > Th. List > pm2.61dc | GIF version |
Description: Case elimination for a decidable proposition. Theorem *2.61 of [WhiteheadRussell] p. 107 under a decidability condition. (Contributed by Jim Kingdon, 29-Mar-2018.) |
Ref | Expression |
---|---|
pm2.61dc | ⊢ (DECID 𝜑 → ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.6dc 848 | . 2 ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜓) → ((𝜑 → 𝜓) → 𝜓))) | |
2 | 1 | com23 78 | 1 ⊢ (DECID 𝜑 → ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 DECID wdc 820 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-dc 821 |
This theorem is referenced by: (None) |
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