This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ φ \to \neg ψ$
	Assertion	pm2.21d	$⊢ φ \to (ψ \to χ)$

Step	Hyp	Ref	Expression
1		pm2.21d.1	$⊢ φ \to \neg ψ$
2	1	a1d	$⊢ φ \to (\neg χ \to \neg ψ)$
3	2	con4d	$⊢ φ \to (ψ \to χ)$