Metamath Proof Explorer


Theorem ord

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994)

Ref Expression
Hypothesis ord.1 ⊢ φ → ψ ∨ χ
Assertion ord ⊢ φ → ¬ ψ → χ

Proof

Step Hyp Ref Expression
1 ord.1 ⊢ φ → ψ ∨ χ
2 df-or ⊢ ψ ∨ χ ↔ ¬ ψ → χ
3 1 2 sylib ⊢ φ → ¬ ψ → χ