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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 |
Ref | Expression |
---|---|
necon3bd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon3bd.1 | . . 3 | |
2 | 1 | con3d 561 | . 2 |
3 | df-ne 2206 | . 2 | |
4 | 2, 3 | syl6ibr 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1243 wne 2204 |
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 |
This theorem depends on definitions: df-bi 110 df-ne 2206 |
This theorem is referenced by: nelne1 2295 nelne2 2296 nssne1 3001 nssne2 3002 disjne 3273 difsn 3501 nbrne1 3781 nbrne2 3782 ac6sfi 6352 indpi 6440 zneo 8339 |
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