How can i show that if Γ∪{φ}⇒ψ and Γ∪{φ}⇒¬ψ then Γ⊨¬φ?

how can i show that if Γ∪{φ}⇒ψ and Γ∪{φ}⇒¬ψ then Γ⊨¬φ?

1 Answer
Aug 12, 2018

See explanation...

Explanation:

Given:

Gamma uu { varphi } => psi" " and " "Gamma uu { varphi } => not psi

we can deduce:

Gamma uu { varphi } => (psi ^^ not psi) => ⊥

So:

Gamma |== (varphi => ⊥)

From which we can deduce:

Gamma |== not varphi