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Theorem pm2.21ddne 2430
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 2368 . 2 (𝜑 → ¬ 𝐴 = 𝐵)
41, 3pm2.21dd 620 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-in2 615
This theorem depends on definitions:  df-bi 117  df-ne 2348
This theorem is referenced by:  npnflt  9813  nmnfgt  9816  xlt2add  9878  xrbdtri  11279  divalglemex  11921  divalg  11923  znege1  12172  ennnfonelemex  12409
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