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Theorem necon2i 2365
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 2330 . 2 (𝐴 = 𝐵 → ¬ 𝐶 = 𝐷)
32necon2ai 2363 1 (𝐶 = 𝐷𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  wne 2309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-ne 2310
This theorem is referenced by:  xleaddadd  9696
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