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Mirrors > Home > NFE Home > Th. List > ordi | Unicode version |
Description: Distributive law for disjunction. Theorem *4.41 of [WhiteheadRussell] p. 119. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 28-Nov-2013.) |
Ref | Expression |
---|---|
ordi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jcab 833 | . 2 | |
2 | df-or 359 | . 2 | |
3 | df-or 359 | . . 3 | |
4 | df-or 359 | . . 3 | |
5 | 3, 4 | anbi12i 678 | . 2 |
6 | 1, 2, 5 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wo 357 wa 358 |
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 177 df-or 359 df-an 360 |
This theorem is referenced by: ordir 835 orddi 839 pm5.63 890 pm4.43 893 cadan 1392 undi 3502 undif4 3607 |
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