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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 Ref
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]
13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |