Theorem con2b 324

Description: Contraposition. Bidirectional version of con2 108. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 108	. 2 ⊢ ((φ → ¬ ψ) → (ψ → ¬ φ))
2		con2 108	. 2 ⊢ ((ψ → ¬ φ) → (φ → ¬ ψ))
3	1, 2	impbii 180	1 ⊢ ((φ → ¬ ψ) ↔ (ψ → ¬ φ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  mt2bi  328  pm4.15  564  nic-ax  1438  nic-axALT  1439  ssconb  3400  disjsn  3787  evenodddisj  4517