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Mirrors > Home > ILE Home > Th. List > necon4ddc | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by Jim Kingdon, 17-May-2018.) |
Ref | Expression |
---|---|
necon4ddc.1 | DECID |
Ref | Expression |
---|---|
necon4ddc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon4ddc.1 | . . 3 DECID | |
2 | df-ne 2246 | . . . 4 | |
3 | df-ne 2246 | . . . 4 | |
4 | 2, 3 | imbi12i 237 | . . 3 |
5 | 1, 4 | syl6ib 159 | . 2 DECID |
6 | condc 782 | . 2 DECID | |
7 | 5, 6 | sylcom 28 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 775 wceq 1284 wne 2245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in2 577 ax-io 662 |
This theorem depends on definitions: df-bi 115 df-dc 776 df-ne 2246 |
This theorem is referenced by: (None) |
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