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Mirrors > Home > ILE Home > Th. List > pm4.66dc | GIF version |
Description: Theorem *4.66 of [WhiteheadRussell] p. 120, given a decidability condition. (Contributed by Jim Kingdon, 2-May-2018.) |
Ref | Expression |
---|---|
pm4.66dc | ⊢ (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.64dc 886 | 1 ⊢ (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 104 ∨ wo 698 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-in1 604 ax-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-dc 821 |
This theorem is referenced by: pm4.54dc 888 |
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