Theorem pm2.18d

Description: Deduction form of the Clavius law pm2.18 . (Contributed by FL, 12-Jul-2009) (Proof shortened by Andrew Salmon, 7-May-2011) Shorten pm2.18 . (Revised by Wolf Lammen, 17-Nov-2023)

	Ref	Expression
Hypothesis	pm2.18d.1	$$⊢\phi \to \left(\neg \psi \to \psi \right)$$
Assertion	pm2.18d	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.18d.1	$$⊢\phi \to \left(\neg \psi \to \psi \right)$$
2		id	$$⊢\phi \to \phi$$
3		pm2.21	$$⊢\neg \psi \to \left(\psi \to \neg \phi \right)$$
4	1 3	sylcom	$$⊢\phi \to \left(\neg \psi \to \neg \phi \right)$$
5	2 4	mt4d	$$⊢\phi \to \psi$$