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Theorem pm2.21dd 550
Description: A contradiction implies anything. Deduction from pm2.21 547. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
pm2.21dd.1 (𝜑𝜓)
pm2.21dd.2 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
pm2.21dd (𝜑𝜒)

Proof of Theorem pm2.21dd
StepHypRef Expression
1 pm2.21dd.1 . 2 (𝜑𝜓)
2 pm2.21dd.2 . . 3 (𝜑 → ¬ 𝜓)
32pm2.21d 549 . 2 (𝜑 → (𝜓𝜒))
41, 3mpd 13 1 (𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 545
This theorem is referenced by:  pm2.21fal  1264  pm2.21ddne  2285  ordtriexmidlem  4241  ordtri2or2exmidlem  4247  onsucelsucexmidlem  4250  nnm00  6089  phpm  6314  fidifsnen  6318  aptiprleml  6718  aptiprlemu  6719  uzdisj  8922  nn0disj  8962  frec2uzlt2d  9068
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