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  1496  nic-ax  1673  nic-axALT  1674  alimex  1831  dfdif3OLD  4118  ssconb  4142  disjsn  4711  oneqmini  6436  kmlem4  10194  isprm3  16720  ssdifidlprm  33486  bnj1171  35014  bnj1176  35019  bnj1204  35026  bnj1388  35047  bnj1523  35085  fvineqsneq  37413  dfxor5  43780  pm13.196a  44433  sswfaxreg  45004