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Mirrors > Home > MPE Home > Th. List > hadbi | Structured version Visualization version Unicode version |
Description: The adder sum is the same as the triple biconditional. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
hadbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1405 |
. 2
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2 | df-had 1496 |
. 2
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3 | xnor 1406 |
. . . 4
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4 | 3 | bibi1i 316 |
. . 3
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5 | nbbn 360 |
. . 3
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6 | 4, 5 | bitri 253 |
. 2
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7 | 1, 2, 6 | 3bitr4i 281 |
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 189 df-xor 1405 df-had 1496 |
This theorem is referenced by: hadnot 1504 had1 1505 |
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