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Theorem necon2i 3048
Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)
Hypothesis
Ref Expression
necon2i.1 (𝐴 = 𝐵𝐶𝐷)
Assertion
Ref Expression
necon2i (𝐶 = 𝐷𝐴𝐵)

Proof of Theorem necon2i
StepHypRef Expression
1 necon2i.1 . . 3 (𝐴 = 𝐵𝐶𝐷)
21neneqd 3019 . 2 (𝐴 = 𝐵 → ¬ 𝐶 = 𝐷)
32necon2ai 3043 1 (𝐶 = 𝐷𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1530  wne 3014
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 209  df-ne 3015
This theorem is referenced by:  cmpfi  22008  mcubic  25417  cubic2  25418  2sqlem11  25997  ovoliunnfl  34921  voliunnfl  34923  volsupnfl  34924  mncn0  39724  aaitgo  39747
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