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Theorem impcon4bid 228
Description: A variation on impbid 213 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 115 . 2 (𝜑 → (𝜒𝜓))
41, 3impbid 213 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207
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 208
This theorem is referenced by:  con4bid  318  soisoi  7076  isomin  7085  alephdom  9499  nn0n0n1ge2b  11955  om2uzlt2i  13312  sadcaddlem  15798  isprm5  16043  pcdvdsb  16197  oexpreposd  39046  cvgdvgrat  40512
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