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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 102 | . . . 4 | |
2 | 1 | orim2i 678 | . . 3 |
3 | simpr 103 | . . . 4 | |
4 | 3 | orim2i 678 | . . 3 |
5 | 2, 4 | jca 290 | . 2 |
6 | orc 633 | . . . 4 | |
7 | 6 | adantl 262 | . . 3 |
8 | 6 | adantr 261 | . . . 4 |
9 | olc 632 | . . . 4 | |
10 | 8, 9 | jaoian 709 | . . 3 |
11 | 7, 10 | jaodan 710 | . 2 |
12 | 5, 11 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: ordir 730 orddi 733 pm5.63dc 853 pm4.43 856 orbididc 860 undi 3185 undif4 3284 elnn1uz2 8544 |
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