Single Idea 13615

[catalogued under 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions]

Full Idea

If a group of formulae prove a conclusion, we can 'conditionalize' this into a chain of separate inferences, which leads to the Deduction Theorem (or Conditional Proof), that 'If Γ,φ|-ψ then Γ|-φ→ψ'.

Clarification

'Conditonalising' involves saying IF this is true then that is true

Gist of Idea

'Conditonalised' inferences point to the Deduction Theorem: 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.203


A Reaction

This is the rule CP (Conditional Proof) which can be found in the rules for propositional logic I transcribed from Lemmon's book.

Related Idea

Idea 9397 CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]