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Mirrors > Home > ILE Home > Th. List > necon2ad | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by NM, 19-Apr-2007.) (Proof rewritten by Jim Kingdon, 16-May-2018.) |
Ref | Expression |
---|---|
necon2ad.1 |
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Ref | Expression |
---|---|
necon2ad |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon2ad.1 |
. . 3
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2 | 1 | con2d 614 |
. 2
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3 | df-ne 2310 |
. 2
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4 | 2, 3 | syl6ibr 161 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 df-ne 2310 |
This theorem is referenced by: necon2d 2368 prneimg 3709 tz7.2 4284 nordeq 4467 pr2ne 7065 ltne 7873 apne 8409 xrltne 9626 npnflt 9628 nmnfgt 9631 ge0nemnf 9637 rpexp 11867 sqrt2irr 11876 |
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