Theorem con1d

Description: A contraposition deduction. (Contributed by NM, 27-Dec-1992)

	Ref	Expression
Hypothesis	con1d.1	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
Assertion	con1d	⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		con1d.1	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
2		notnot	⊢ ( 𝜒 → ¬ ¬ 𝜒 )
3	1 2	syl6	⊢ ( 𝜑 → ( ¬ 𝜓 → ¬ ¬ 𝜒 ) )
4	3	con4d	⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) )