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Mirrors > Home > ILE Home > Th. List > 3ioran | Unicode version |
Description: Negated triple disjunction as triple conjunction. (Contributed by Scott Fenton, 19-Apr-2011.) |
Ref | Expression |
---|---|
3ioran |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ioran 742 |
. . 3
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2 | 1 | anbi1i 454 |
. 2
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3 | ioran 742 |
. . 3
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4 | df-3or 964 |
. . 3
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5 | 3, 4 | xchnxbir 671 |
. 2
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6 | df-3an 965 |
. 2
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7 | 2, 5, 6 | 3bitr4i 211 |
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-3or 964 df-3an 965 |
This theorem is referenced by: ne3anior 2397 |
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