Theorem tsim3

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

	Ref	Expression
Assertion	tsim3	$$⊢\theta \to \left(\neg \psi \vee \left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\psi \to \left(\phi \to \psi \right)$$
2	1	imori	$$⊢\left(\neg \psi \vee \left(\phi \to \psi \right)\right)$$
3	2	a1i	$$⊢\theta \to \left(\neg \psi \vee \left(\phi \to \psi \right)\right)$$