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Theorem pm2.21ddne 2866
 Description: A contradiction implies anything. Equality/inequality deduction form. (Contributed by David Moews, 28-Feb-2017.)
Hypotheses
Ref Expression
pm2.21ddne.1 (𝜑𝐴 = 𝐵)
pm2.21ddne.2 (𝜑𝐴𝐵)
Assertion
Ref Expression
pm2.21ddne (𝜑𝜓)

Proof of Theorem pm2.21ddne
StepHypRef Expression
1 pm2.21ddne.1 . 2 (𝜑𝐴 = 𝐵)
2 pm2.21ddne.2 . . 3 (𝜑𝐴𝐵)
32neneqd 2787 . 2 (𝜑 → ¬ 𝐴 = 𝐵)
41, 3pm2.21dd 185 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ≠ wne 2780 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 196  df-ne 2782 This theorem is referenced by:  cshwshashlem2  15641  dprdsn  18258  coseq00topi  24058  tglndim0  25324  ncolncol  25341  footne  25415  sgnsub  29933  sgnmulsgn  29938  sgnmulsgp  29939  pconcon  30467  osumcllem11N  34270  dochexmidlem8  35774  fnchoice  38211
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