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Mirrors > Home > ILE Home > Th. List > pm4.64dc | GIF version |
Description: Theorem *4.64 of [WhiteheadRussell] p. 120, given a decidability condition. The reverse direction, pm2.53 722, holds for all propositions. (Contributed by Jim Kingdon, 2-May-2018.) |
Ref | Expression |
---|---|
pm4.64dc | ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfordc 892 | . 2 ⊢ (DECID 𝜑 → ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))) | |
2 | 1 | bicomd 141 | 1 ⊢ (DECID 𝜑 → ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 105 ∨ wo 708 DECID wdc 834 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-dc 835 |
This theorem is referenced by: pm4.66dc 901 |
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