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  4084  ssconb  4108  disjsn  4678  oneqmini  6388  kmlem4  10114  isprm3  16660  ssdifidlprm  33436  bnj1171  34997  bnj1176  35002  bnj1204  35009  bnj1388  35030  bnj1523  35068  fvineqsneq  37407  dfxor5  43763  pm13.196a  44410  sswfaxreg  44984