Theorem con2b 359

Description: Contraposition. Bidirectional version of con2 135. (Contributed by NM, 12-Mar-1993.)

Assertion

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

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 135	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2		con2 135	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
3	1, 2	impbii 209	1 ⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 206

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 207

This theorem is referenced by:  mt2bi  363  pm4.15  832  nancom  1496  nic-ax  1673  nic-axALT  1674  alimex  1831  dfdif3OLD  4081  ssconb  4105  disjsn  4675  oneqmini  6385  kmlem4  10107  isprm3  16653  ssdifidlprm  33429  bnj1171  34990  bnj1176  34995  bnj1204  35002  bnj1388  35023  bnj1523  35061  fvineqsneq  37400  dfxor5  43756  pm13.196a  44403  sswfaxreg  44977