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Mirrors > Home > ILE Home > Th. List > necon1bddc | Unicode version |
Description: Contrapositive deduction for inequality. (Contributed by Jim Kingdon, 19-May-2018.) |
Ref | Expression |
---|---|
necon1bddc.1 | DECID |
Ref | Expression |
---|---|
necon1bddc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon1bddc.1 | . . 3 DECID | |
2 | df-ne 2328 | . . . 4 | |
3 | 2 | imbi1i 237 | . . 3 |
4 | 1, 3 | syl6ib 160 | . 2 DECID |
5 | con1dc 842 | . 2 DECID | |
6 | 4, 5 | sylcom 28 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 820 wceq 1335 wne 2327 |
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 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-stab 817 df-dc 821 df-ne 2328 |
This theorem is referenced by: necon1ddc 2405 |
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