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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 |
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Ref | Expression |
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necon1bidc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2310 |
. . 3
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2 | necon1bidc.1 |
. . 3
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3 | 1, 2 | syl5bir 152 |
. 2
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4 | con1dc 842 |
. 2
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5 | 3, 4 | mpd 13 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 2310 |
This theorem is referenced by: (None) |
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