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  4059  ssconb  4083  disjsn  4656  oneqmini  6368  kmlem4  10065  isprm3  16611  ssdifidlprm  33523  bnj1171  35148  bnj1176  35153  bnj1204  35160  bnj1388  35181  bnj1523  35219  regsfromsetind  36727  fvineqsneq  37724  dfxor5  44197  pm13.196a  44844  sswfaxreg  45417