Axiom ax-frege28

Description: Contraposition. Identical to con3 . Theorem *2.16 of WhiteheadRussell p. 103. Axiom 28 of Frege1879 p. 43. (Contributed by RP, 24-Dec-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-frege28	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		wph	⊢ 𝜑
1		wps	⊢ 𝜓
2	0 1	wi	⊢ ( 𝜑 → 𝜓 )
3	1	wn	⊢ ¬ 𝜓
4	0	wn	⊢ ¬ 𝜑
5	3 4	wi	⊢ ( ¬ 𝜓 → ¬ 𝜑 )
6	2 5	wi	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )