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Theorem necon4i 2812
Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 24-Nov-2019.)
Hypothesis
Ref Expression
necon4i.1 (𝐴𝐵𝐶𝐷)
Assertion
Ref Expression
necon4i (𝐶 = 𝐷𝐴 = 𝐵)

Proof of Theorem necon4i
StepHypRef Expression
1 necon4i.1 . . 3 (𝐴𝐵𝐶𝐷)
21neneqd 2782 . 2 (𝐴𝐵 → ¬ 𝐶 = 𝐷)
32necon4ai 2808 1 (𝐶 = 𝐷𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1474  wne 2775
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 195  df-ne 2777
This theorem is referenced by:  unixp0  5568  scott0  8605  nn0opthi  12870
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