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Mirrors > Home > NFE Home > Th. List > ecase3d | GIF version |
Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
Ref | Expression |
---|---|
ecase3d.1 | ⊢ (φ → (ψ → θ)) |
ecase3d.2 | ⊢ (φ → (χ → θ)) |
ecase3d.3 | ⊢ (φ → (¬ (ψ ∨ χ) → θ)) |
Ref | Expression |
---|---|
ecase3d | ⊢ (φ → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecase3d.1 | . . 3 ⊢ (φ → (ψ → θ)) | |
2 | ecase3d.2 | . . 3 ⊢ (φ → (χ → θ)) | |
3 | 1, 2 | jaod 369 | . 2 ⊢ (φ → ((ψ ∨ χ) → θ)) |
4 | ecase3d.3 | . 2 ⊢ (φ → (¬ (ψ ∨ χ) → θ)) | |
5 | 3, 4 | pm2.61d 150 | 1 ⊢ (φ → θ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 357 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-or 359 |
This theorem is referenced by: ecased 910 |
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