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Theorem necon3ai 2248
Description: Contrapositive inference for inequality. (Contributed by NM, 23-May-2007.) (Proof rewritten by Jim Kingdon, 15-May-2018.)
Hypothesis
Ref Expression
necon3ai.1
Assertion
Ref Expression
necon3ai  =/=

Proof of Theorem necon3ai
StepHypRef Expression
1 df-ne 2203 . 2  =/=
2 necon3ai.1 . . 3
32con3i 561 . 2
41, 3sylbi 114 1  =/=
Colors of variables: wff set class
Syntax hints:   wn 3   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-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by:  disjsn2  3424  0nelxp  4315  fvunsng  5300
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