Theorem tsan1

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

	Ref	Expression
Assertion	tsan1	$$⊢\theta \to \left(\left(\neg \phi \vee \neg \psi \right)\vee \left(\phi \wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.12	$$⊢\left(\left(\neg \phi \vee \neg \psi \right)\vee \left(\phi \wedge \psi \right)\right)$$
2	1	a1i	$$⊢\theta \to \left(\left(\neg \phi \vee \neg \psi \right)\vee \left(\phi \wedge \psi \right)\right)$$