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Theorem necon3ai 2556
Description: Contrapositive inference for inequality. (Contributed by NM, 23-May-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
necon3ai.1
Assertion
Ref Expression
necon3ai

Proof of Theorem necon3ai
StepHypRef Expression
1 necon3ai.1 . . 3
2 nne 2520 . . 3
31, 2sylibr 203 . 2
43con2i 112 1
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:  disjsn2  3787  fvunsn  5444  enadjlem1  6059  enadj  6060
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