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  4093  ssconb  4117  disjsn  4687  oneqmini  6405  kmlem4  10168  isprm3  16702  ssdifidlprm  33473  bnj1171  35031  bnj1176  35036  bnj1204  35043  bnj1388  35064  bnj1523  35102  fvineqsneq  37430  dfxor5  43791  pm13.196a  44438  sswfaxreg  45012