MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  impcon4bid Structured version   Visualization version   GIF version

Theorem impcon4bid 215
Description: A variation on impbid 200 with contraposition. (Contributed by Jeff Hankins, 3-Jul-2009.)
Hypotheses
Ref Expression
impcon4bid.1 (𝜑 → (𝜓𝜒))
impcon4bid.2 (𝜑 → (¬ 𝜓 → ¬ 𝜒))
Assertion
Ref Expression
impcon4bid (𝜑 → (𝜓𝜒))

Proof of Theorem impcon4bid
StepHypRef Expression
1 impcon4bid.1 . 2 (𝜑 → (𝜓𝜒))
2 impcon4bid.2 . . 3 (𝜑 → (¬ 𝜓 → ¬ 𝜒))
32con4d 112 . 2 (𝜑 → (𝜒𝜓))
41, 3impbid 200 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 194
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 195
This theorem is referenced by:  con4bid  305  soisoi  6456  isomin  6465  alephdom  8764  nn0n0n1ge2b  11206  om2uzlt2i  12567  sadcaddlem  14963  isprm5  15203  pcdvdsb  15357  cvgdvgrat  37330
  Copyright terms: Public domain W3C validator