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Mirrors > Home > ILE Home > Th. List > necon1bidc | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by Jim Kingdon, 15-May-2018.) |
Ref | Expression |
---|---|
necon1bidc.1 | DECID |
Ref | Expression |
---|---|
necon1bidc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2206 | . . 3 | |
2 | necon1bidc.1 | . . 3 DECID | |
3 | 1, 2 | syl5bir 142 | . 2 DECID |
4 | con1dc 753 | . 2 DECID | |
5 | 3, 4 | mpd 13 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 742 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 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 df-ne 2206 |
This theorem is referenced by: (None) |
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