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Mirrors > Home > NFE Home > Th. List > cadbi123d | Unicode version |
Description: Equality theorem for adder carry. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
hadbid.1 |
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hadbid.2 |
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hadbid.3 |
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Ref | Expression |
---|---|
cadbi123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hadbid.1 |
. . . 4
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2 | hadbid.2 |
. . . 4
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3 | 1, 2 | anbi12d 691 |
. . 3
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4 | hadbid.3 |
. . . 4
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5 | 1, 2 | xorbi12d 1315 |
. . . 4
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6 | 4, 5 | anbi12d 691 |
. . 3
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7 | 3, 6 | orbi12d 690 |
. 2
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8 | df-cad 1381 |
. 2
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9 | df-cad 1381 |
. 2
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10 | 7, 8, 9 | 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: cadbi123i 1385 |
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