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Mirrors > Home > ILE Home > Th. List > ne3anior | Unicode version |
Description: A De Morgan's law for inequality. (Contributed by NM, 30-Sep-2013.) (Proof rewritten by Jim Kingdon, 19-May-2018.) |
Ref | Expression |
---|---|
ne3anior |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2348 |
. . 3
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2 | df-ne 2348 |
. . 3
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3 | df-ne 2348 |
. . 3
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4 | 1, 2, 3 | 3anbi123i 1188 |
. 2
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5 | 3ioran 993 |
. 2
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6 | 4, 5 | bitr4i 187 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-ne 2348 |
This theorem is referenced by: eldiftp 3637 |
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