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Mirrors > Home > ILE Home > Th. List > necon1abiddc | Unicode version |
Description: Contrapositive deduction for inequality. (Contributed by Jim Kingdon, 16-May-2018.) |
Ref | Expression |
---|---|
necon1abiddc.1 | DECID |
Ref | Expression |
---|---|
necon1abiddc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon1abiddc.1 | . . 3 DECID | |
2 | 1 | con1biddc 871 | . 2 DECID |
3 | df-ne 2341 | . . 3 | |
4 | 3 | bibi1i 227 | . 2 |
5 | 2, 4 | syl6ibr 161 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 DECID wdc 829 wceq 1348 wne 2340 |
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 609 ax-in2 610 ax-io 704 |
This theorem depends on definitions: df-bi 116 df-stab 826 df-dc 830 df-ne 2341 |
This theorem is referenced by: necon2abiddc 2406 |
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