Theorem con2b 348

Description: Contraposition. Bidirectional version of con2 130. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
con2b	⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 130	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2		con2 130	. 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
3	1, 2	impbii 199	1 ⊢ ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 196

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 197

This theorem is referenced by:  mt2bi  352  pm4.15  604  nic-ax  1638  nic-axALT  1639  alimex  1798  ssconb  3776  disjsn  4278  oneqmini  5814  kmlem4  9013  isprm3  15443  bnj1171  31194  bnj1176  31199  bnj1204  31206  bnj1388  31227  bnj1523  31265  wl-nancom  33427  dfxor5  38376  pm13.196a  38932