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Mirrors > Home > MPE Home > Th. List > 3anor | Structured version Visualization version Unicode version |
Description: Triple conjunction expressed in terms of triple disjunction. (Contributed by Jeff Hankins, 15-Aug-2009.) |
Ref | Expression |
---|---|
3anor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 987 |
. 2
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2 | anor 492 |
. . . 4
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3 | ianor 491 |
. . . . 5
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4 | 3 | orbi1i 523 |
. . . 4
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5 | 2, 4 | xchbinx 312 |
. . 3
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6 | df-3or 986 |
. . 3
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7 | 5, 6 | xchbinxr 313 |
. 2
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8 | 1, 7 | bitri 253 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 |
This theorem is referenced by: 3ianor 1002 ne3anior 2717 |
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