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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 1039 | . 2 | |
2 | anor 510 | . . . 4 | |
3 | ianor 509 | . . . . 5 | |
4 | 3 | orbi1i 542 | . . . 4 |
5 | 2, 4 | xchbinx 324 | . . 3 |
6 | df-3or 1038 | . . 3 | |
7 | 5, 6 | xchbinxr 325 | . 2 |
8 | 1, 7 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wo 383 wa 384 w3o 1036 w3a 1037 |
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 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 |
This theorem is referenced by: 3ianor 1055 ne3anior 2887 |
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