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Theorem necon4i 2576
Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
necon4i.1 (ABCD)
Assertion
Ref Expression
necon4i (C = DA = B)

Proof of Theorem necon4i
StepHypRef Expression
1 necon4i.1 . . 3 (ABCD)
21necon2bi 2562 . 2 (C = D → ¬ AB)
3 nne 2520 . 2 ABA = B)
42, 3sylib 188 1 (C = DA = B)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1642  wne 2516
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 177  df-ne 2518
This theorem is referenced by:  pw10b  4166  map0  6025
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