![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > sylan2 | GIF version |
Description: A syllogism inference. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Nov-2012.) |
Ref | Expression |
---|---|
sylan2.1 | ⊢ (φ → χ) |
sylan2.2 | ⊢ ((ψ ∧ χ) → θ) |
Ref | Expression |
---|---|
sylan2 | ⊢ ((ψ ∧ φ) → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan2.1 | . . 3 ⊢ (φ → χ) | |
2 | 1 | adantl 262 | . 2 ⊢ ((ψ ∧ φ) → χ) |
3 | sylan2.2 | . 2 ⊢ ((ψ ∧ χ) → θ) | |
4 | 2, 3 | syldan 266 | 1 ⊢ ((ψ ∧ φ) → θ) |
Copyright terms: Public domain | W3C validator |