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  1497  nic-ax  1674  nic-axALT  1675  alimex  1832  dfdif3OLD  4068  ssconb  4092  disjsn  4664  oneqmini  6359  kmlem4  10042  isprm3  16591  ssdifidlprm  33418  bnj1171  35007  bnj1176  35012  bnj1204  35019  bnj1388  35040  bnj1523  35078  fvineqsneq  37445  dfxor5  43799  pm13.196a  44446  sswfaxreg  45019