Database: Weakening rule for implication

Proposition 76: Weakening rule for implication (inference rule)

Given that \psi holds, we may infer that the implication (\phi \Rightarrow \psi) holds: \cfrac{\vdash \psi}{\vdash (\phi \Rightarrow \psi)}.

Proof: By weakening, we infer \phi entails \psi . Thus, by conditional introduction, we get that (\phi \Rightarrow \psi) holds. \square

This database entry builds on the following:

  1. Definition: Implication
  2. Terminology: Inference rule
  3. Theorem: The weakening rule
  4. Theorem: Conditional introduction