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Theorem necon2i 2255
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 2221 . 2 (A = B → ¬ 𝐶 = 𝐷)
32necon2ai 2253 1 (𝐶 = 𝐷AB)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by: (None)
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