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Mirrors > Home > ILE Home > Th. List > imorr | GIF version |
Description: Implication in terms of disjunction. One direction of theorem *4.6 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as seen at imordc 837. (Contributed by Jim Kingdon, 21-Jul-2018.) |
Ref | Expression |
---|---|
imorr | ⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-in2 583 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
2 | ax-1 5 | . 2 ⊢ (𝜓 → (𝜑 → 𝜓)) | |
3 | 1, 2 | jaoi 674 | 1 ⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 667 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 583 ax-io 668 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: pm4.52im 844 nf4r 1613 |
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