Theorem con2b 593

Description: Contraposition. Bidirectional version of con2 572. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con2b	⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 572	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2		con2 572	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
3	1, 2	impbii 117	1 ⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  mt2bi  609  pm4.15  789  ssconb  3076  disjsn  3432