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  4067  ssconb  4091  disjsn  4663  oneqmini  6364  kmlem4  10052  isprm3  16596  ssdifidlprm  33430  bnj1171  35033  bnj1176  35038  bnj1204  35045  bnj1388  35066  bnj1523  35104  fvineqsneq  37477  dfxor5  43884  pm13.196a  44531  sswfaxreg  45104