Single Idea 13356

[catalogued under 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL]

Full Idea

The Conditional Principle says that Γ |= φ→ψ iff Γ,φ |= ψ. With the addition of negation, this implies φ,φ→ψ |= ψ, which is 'modus ponens'.

Gist of Idea

The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ

Source

David Bostock (Intermediate Logic [1997], 2.5.H)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.33

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A Reaction

[Second half is in Ex. 2.5.4]