MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con2b Structured version   Visualization version   GIF version

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
StepHypRef Expression
1 con2 130 . 2 ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2 con2 130 . 2 ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
31, 2impbii 199 1 ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))
Colors of variables: wff setvar class
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  606  nic-ax  1747  nic-axALT  1748  alimex  1907  dfdif3  3863  ssconb  3886  disjsn  4390  oneqmini  5937  kmlem4  9187  isprm3  15618  bnj1171  31396  bnj1176  31401  bnj1204  31408  bnj1388  31429  bnj1523  31467  wl-nancom  33628  dfxor5  38579  pm13.196a  39135
  Copyright terms: Public domain W3C validator