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Theorem necon4ai 2695
Description: Contrapositive inference for inequality. (Contributed by NM, 16-Jan-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 22-Nov-2019.)
Hypothesis
Ref Expression
necon4ai.1
Assertion
Ref Expression
necon4ai

Proof of Theorem necon4ai
StepHypRef Expression
1 notnot1 122 . 2
2 necon4ai.1 . . 3
32necon1bi 2690 . 2
41, 3syl 16 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  =wceq 1395  =/=wne 2652
This theorem is referenced by:  necon4i  2701  dmsn0el  5482  cfeq0  8657
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 185  df-ne 2654
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