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Mirrors > Home > ILE Home > Th. List > ordi | Unicode version |
Description: Distributive law for disjunction. Theorem *4.41 of [WhiteheadRussell] p. 119. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ordi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . . 4 | |
2 | 1 | orim2i 756 | . . 3 |
3 | simpr 109 | . . . 4 | |
4 | 3 | orim2i 756 | . . 3 |
5 | 2, 4 | jca 304 | . 2 |
6 | orc 707 | . . . 4 | |
7 | 6 | adantl 275 | . . 3 |
8 | 6 | adantr 274 | . . . 4 |
9 | olc 706 | . . . 4 | |
10 | 8, 9 | jaoian 790 | . . 3 |
11 | 7, 10 | jaodan 792 | . 2 |
12 | 5, 11 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wo 703 |
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 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ordir 812 orddi 815 pm5.63dc 941 pm4.43 944 orbididc 948 undi 3375 undif4 3477 elnn1uz2 9566 |
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