ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.21dd Structured version   GIF version

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  1263  pm2.21ddne  2282  ordtriexmidlem  4208  onsucelsucexmidlem  4214  nnm00  6038  aptiprleml  6610  aptiprlemu  6611  uzdisj  8705  nn0disj  8745  frec2uzlt2d  8851
  Copyright terms: Public domain W3C validator