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Mirrors > Home > ILE Home > Th. List > pm4.81dc | GIF version |
Description: Theorem *4.81 of [WhiteheadRussell] p. 122, for decidable propositions. This one needs a decidability condition, but compare with pm4.8 623 which holds for all propositions. (Contributed by Jim Kingdon, 4-Jul-2018.) |
Ref | Expression |
---|---|
pm4.81dc | ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜑) ↔ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.18dc 750 | . 2 ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜑) → 𝜑)) | |
2 | pm2.24 551 | . 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜑)) | |
3 | 1, 2 | impbid1 130 | 1 ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜑) ↔ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 98 DECID wdc 742 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 |
This theorem is referenced by: (None) |
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