Theorem pm2.21d

Description: A contradiction implies anything. Deduction associated with pm2.21 . (Contributed by NM, 10-Feb-1996)

	Ref	Expression
Hypothesis	pm2.21d.1	$$⊢\phi \to \neg \psi$$
Assertion	pm2.21d	$$⊢\phi \to \left(\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21d.1	$$⊢\phi \to \neg \psi$$
2	1	a1d	$$⊢\phi \to \left(\neg \chi \to \neg \psi \right)$$
3	2	con4d	$$⊢\phi \to \left(\psi \to \chi \right)$$