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Metamath Proof Explorer

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	$⊢ φ \to (\neg ψ \to ψ)$
	Assertion	pm2.18d	$⊢ φ \to ψ$

Proof

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