Theorem con2d

Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993)

	Ref	Expression
Hypothesis	con2d.1	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
Assertion	con2d	⊢ ( 𝜑 → ( 𝜒 → ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		con2d.1	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
2		notnotr	⊢ ( ¬ ¬ 𝜓 → 𝜓 )
3	2 1	syl5	⊢ ( 𝜑 → ( ¬ ¬ 𝜓 → ¬ 𝜒 ) )
4	3	con4d	⊢ ( 𝜑 → ( 𝜒 → ¬ 𝜓 ) )