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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 621 | . 2 |
3 | df-ne 2335 | . 2 | |
4 | 2, 3 | syl6ibr 161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1342 wne 2334 |
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 2335 |
This theorem is referenced by: nelne1 2424 nelne2 2425 nssne1 3195 nssne2 3196 disjne 3457 difsn 3704 nbrne1 3995 nbrne2 3996 ac6sfi 6855 indpi 7274 zneo 9283 pc2dvds 12240 pcadd 12250 oddprmdvds 12263 |
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