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Mirrors > Home > ILE Home > Th. List > necon3bd | Unicode version |
Description: Contrapositive law deduction for inequality. (Contributed by NM, 2-Apr-2007.) (Proof rewritten by Jim Kingdon, 15-May-2018.) |
Ref | Expression |
---|---|
necon3bd.1 |
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Ref | Expression |
---|---|
necon3bd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon3bd.1 |
. . 3
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2 | 1 | con3d 594 |
. 2
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3 | df-ne 2250 |
. 2
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4 | 2, 3 | syl6ibr 160 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 |
This theorem depends on definitions: df-bi 115 df-ne 2250 |
This theorem is referenced by: nelne1 2339 nelne2 2340 nssne1 3066 nssne2 3067 disjne 3318 difsn 3548 nbrne1 3828 nbrne2 3829 ac6sfi 6544 indpi 6804 zneo 8743 |
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