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 ) )