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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 102 |
. . . 4
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2 | 1 | orim2i 677 |
. . 3
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3 | simpr 103 |
. . . 4
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4 | 3 | orim2i 677 |
. . 3
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5 | 2, 4 | jca 290 |
. 2
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6 | orc 632 |
. . . 4
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7 | 6 | adantl 262 |
. . 3
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8 | 6 | adantr 261 |
. . . 4
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9 | olc 631 |
. . . 4
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10 | 8, 9 | jaoian 708 |
. . 3
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11 | 7, 10 | jaodan 709 |
. 2
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12 | 5, 11 | impbii 117 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: ordir 729 orddi 732 pm5.63dc 852 pm4.43 855 orbididc 859 undi 3179 undif4 3278 elnn1uz2 8320 |
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