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Mirrors > Home > ILE Home > Th. List > 3orbi123d | Unicode version |
Description: Deduction joining 3 equivalences to form equivalence of disjunctions. (Contributed by NM, 20-Apr-1994.) |
Ref | Expression |
---|---|
bi3d.1 |
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bi3d.2 |
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bi3d.3 |
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Ref | Expression |
---|---|
3orbi123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi3d.1 |
. . . 4
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2 | bi3d.2 |
. . . 4
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3 | 1, 2 | orbi12d 783 |
. . 3
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4 | bi3d.3 |
. . 3
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5 | 3, 4 | orbi12d 783 |
. 2
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6 | df-3or 964 |
. 2
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7 | df-3or 964 |
. 2
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8 | 5, 6, 7 | 3bitr4g 222 |
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-io 699 |
This theorem depends on definitions: df-bi 116 df-3or 964 |
This theorem is referenced by: ordtriexmid 4445 wetriext 4499 nntri3or 6397 tridc 6801 ltsopi 7152 pitri3or 7154 nqtri3or 7228 elz 9080 ztri3or 9121 qtri3or 10051 trilpo 13411 trirec0 13412 |
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