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 → ¬ 𝜓 )
Assertion	pm2.21d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.21d.1	⊢ ( 𝜑 → ¬ 𝜓 )
2	1	a1d	⊢ ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) )
3	2	con4d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )