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Mirrors > Home > NFE Home > Th. List > cad1 | Unicode version |
Description: If one parameter is true, the adder carry is true exactly when at least one of the other parameters is true. (Contributed by Mario Carneiro, 8-Sep-2016.) |
Ref | Expression |
---|---|
cad1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibar 490 |
. . . 4
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2 | 1 | bicomd 192 |
. . 3
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3 | 2 | orbi2d 682 |
. 2
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4 | df-cad 1381 |
. 2
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5 | pm5.63 890 |
. . 3
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6 | olc 373 |
. . . 4
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7 | orc 374 |
. . . . . 6
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8 | 7 | adantr 451 |
. . . . 5
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9 | id 19 |
. . . . 5
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10 | 8, 9 | jaoi 368 |
. . . 4
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11 | 6, 10 | impbii 180 |
. . 3
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12 | xor2 1310 |
. . . . 5
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13 | ancom 437 |
. . . . 5
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14 | 12, 13 | bitri 240 |
. . . 4
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15 | 14 | orbi2i 505 |
. . 3
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16 | 5, 11, 15 | 3bitr4i 268 |
. 2
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17 | 3, 4, 16 | 3bitr4g 279 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 df-xor 1305 df-cad 1381 |
This theorem is referenced by: (None) |
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