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Mirrors > Home > NFE Home > Th. List > necon3ai | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by NM, 23-May-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
necon3ai.1 |
Ref | Expression |
---|---|
necon3ai |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon3ai.1 | . . 3 | |
2 | nne 2520 | . . 3 | |
3 | 1, 2 | sylibr 203 | . 2 |
4 | 3 | con2i 112 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wceq 1642 wne 2516 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-ne 2518 |
This theorem is referenced by: disjsn2 3787 fvunsn 5444 enadjlem1 6059 enadj 6060 |
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