Metamath Proof Explorer


Theorem con1

Description: Contraposition. Theorem *2.15 of WhiteheadRussell p. 102. Its associated inference is con1i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 12-Feb-2013)

Ref Expression
Assertion con1 ( ( ¬ 𝜑𝜓 ) → ( ¬ 𝜓𝜑 ) )

Proof

Step Hyp Ref Expression
1 id ( ( ¬ 𝜑𝜓 ) → ( ¬ 𝜑𝜓 ) )
2 1 con1d ( ( ¬ 𝜑𝜓 ) → ( ¬ 𝜓𝜑 ) )