Theorem tsan3

Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)

	Ref	Expression
Assertion	tsan3	$$⊢\theta \to \left(\psi \vee \neg \left(\phi \wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.14	$$⊢\left(\neg \phi \vee \neg \psi \right)\to \neg \left(\phi \wedge \psi \right)$$
2	1	olcs	$$⊢\neg \psi \to \neg \left(\phi \wedge \psi \right)$$
3	2	orri	$$⊢\left(\psi \vee \neg \left(\phi \wedge \psi \right)\right)$$
4	3	a1i	$$⊢\theta \to \left(\psi \vee \neg \left(\phi \wedge \psi \right)\right)$$