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Theorem necon2abiidc 2263
Description: Contrapositive inference for inequality. (Contributed by Jim Kingdon, 16-May-2018.)
Hypothesis
Ref Expression
necon2abiidc.1 DECID
Assertion
Ref Expression
necon2abiidc DECID  =/=

Proof of Theorem necon2abiidc
StepHypRef Expression
1 necon2abiidc.1 . . . 4 DECID
21bicomd 129 . . 3 DECID
32necon1abiidc 2259 . 2 DECID  =/=
43bicomd 129 1 DECID  =/=
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wb 98  DECID wdc 741   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  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742  df-ne 2203
This theorem is referenced by: (None)
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