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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 |
. . . 4
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2 | 1 | orim2i 751 |
. . 3
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3 | simpr 109 |
. . . 4
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4 | 3 | orim2i 751 |
. . 3
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5 | 2, 4 | jca 304 |
. 2
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6 | orc 702 |
. . . 4
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7 | 6 | adantl 275 |
. . 3
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8 | 6 | adantr 274 |
. . . 4
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9 | olc 701 |
. . . 4
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10 | 8, 9 | jaoian 785 |
. . 3
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11 | 7, 10 | jaodan 787 |
. 2
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12 | 5, 11 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 699 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ordir 807 orddi 810 pm5.63dc 931 pm4.43 934 orbididc 938 undi 3329 undif4 3430 elnn1uz2 9428 |
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