Single Idea 13354

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

Full Idea

The Principle of Conjunction says that Γ |= φ∧ψ iff Γ |= φ and Γ |= ψ. This implies φ,ψ |= φ∧ψ, which is ∧-introduction. It is also implies ∧-elimination.

Gist of Idea

'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ

Source

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

Book Reference

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


A Reaction

[Second half is Ex. 2.5.3] That is, if they are entailed separately, they are entailed as a unit. It is a moot point whether these principles are theorems of propositional logic, or derivation rules.