Metamath Proof Explorer


Theorem con2

Description: Contraposition. Theorem *2.03 of WhiteheadRussell p. 100. (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 12-Feb-2013)

Ref Expression
Assertion con2 ( ( 𝜑 → ¬ 𝜓 ) → ( 𝜓 → ¬ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 id ( ( 𝜑 → ¬ 𝜓 ) → ( 𝜑 → ¬ 𝜓 ) )
2 1 con2d ( ( 𝜑 → ¬ 𝜓 ) → ( 𝜓 → ¬ 𝜑 ) )