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Mirrors > Home > ILE Home > Th. List > sylc | GIF version |
Description: A syllogism inference combined with contraction. (Contributed by NM, 4-May-1994.) (Revised by NM, 13-Jul-2013.) |
Ref | Expression |
---|---|
sylc.1 | ⊢ (φ → ψ) |
sylc.2 | ⊢ (φ → χ) |
sylc.3 | ⊢ (ψ → (χ → θ)) |
Ref | Expression |
---|---|
sylc | ⊢ (φ → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylc.1 | . . 3 ⊢ (φ → ψ) | |
2 | sylc.2 | . . 3 ⊢ (φ → χ) | |
3 | sylc.3 | . . 3 ⊢ (ψ → (χ → θ)) | |
4 | 1, 2, 3 | syl2im 34 | . 2 ⊢ (φ → (φ → θ)) |
5 | 4 | pm2.43i 43 | 1 ⊢ (φ → θ) |
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