Metamath Proof Explorer


Theorem con1d

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

Ref Expression
Hypothesis con1d.1 ( 𝜑 → ( ¬ 𝜓𝜒 ) )
Assertion con1d ( 𝜑 → ( ¬ 𝜒𝜓 ) )

Proof

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