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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 | hadd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1465 | . 2 | |
2 | df-had 1533 | . 2 hadd | |
3 | xnor 1466 | . . . 4 | |
4 | 3 | bibi1i 328 | . . 3 |
5 | nbbn 373 | . . 3 | |
6 | 4, 5 | bitri 264 | . 2 |
7 | 1, 2, 6 | 3bitr4i 292 | 1 hadd |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wxo 1464 haddwhad 1532 |
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 197 df-xor 1465 df-had 1533 |
This theorem is referenced by: hadnot 1541 had1 1542 |
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