Example of a difficult derivation
Roll your own derivations
You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]
You will need to use the correct logical symbols. Here they are
F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴ (or use the palette to produce them)
Tutorial 25 Exercises h
Tutorial 25 Exercises g
Tutorial 25 Exercises e
Tutorial 25 Exercises d
Skill to be acquired:
To understand how the various restrictions on the quantificational rules work to exclude certain kinds of invalid inferences
Bergmann The Logic Book Section 10.1
The Rule of Universal Elimination UE
If a derivation contains a line of the form
n (∀<variable>)<scope> <any justification>
then a line of the form
Bergmann The Logic Book Section 10.1.
Existential Elimination (often called 'Existential Instantiation') permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. It is one of those rules which involves the adoption and dropping of an extra assumption (like ∼I,⊃I,∨E, and ≡I).
The circumstance that Existential Instantiation gets invoked looks like this.