Single Idea 13617

[catalogued under 5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens]

Full Idea

Modus Ponens is equivalent to the converse of the Deduction Theorem, namely 'If Γ |- φ→ψ then Γ,φ|-ψ'.

Gist of Idea

MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ

Source

David Bostock (Intermediate Logic [1997], 5.3)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.207


A Reaction

See 13615 for details of the Deduction Theorem. See 13614 for Modus Ponens.

Related Ideas

Idea 13615 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]

Idea 13614 MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock]