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  833  nancom  1498  nic-ax  1675  nic-axALT  1676  alimex  1833  dfdif3OLD  4072  ssconb  4096  disjsn  4670  oneqmini  6378  kmlem4  10076  isprm3  16622  ssdifidlprm  33550  bnj1171  35175  bnj1176  35180  bnj1204  35187  bnj1388  35208  bnj1523  35246  regsfromsetind  36688  fvineqsneq  37661  dfxor5  44117  pm13.196a  44764  sswfaxreg  45337