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Mirrors > Home > ILE Home > Th. List > sylancl | GIF version |
Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
sylancl.1 | ⊢ (φ → ψ) |
sylancl.2 | ⊢ χ |
sylancl.3 | ⊢ ((ψ ∧ χ) → θ) |
Ref | Expression |
---|---|
sylancl | ⊢ (φ → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylancl.1 | . 2 ⊢ (φ → ψ) | |
2 | sylancl.2 | . . 3 ⊢ χ | |
3 | 2 | a1i 9 | . 2 ⊢ (φ → χ) |
4 | sylancl.3 | . 2 ⊢ ((ψ ∧ χ) → θ) | |
5 | 1, 3, 4 | syl2anc 391 | 1 ⊢ (φ → θ) |
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