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Mirrors > Home > MPE Home > Th. List > hadcomb | Structured version Visualization version Unicode version |
Description: Commutative law for the adders sum. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
hadcomb | hadd hadd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biid 251 | . . 3 | |
2 | xorcom 1467 | . . 3 | |
3 | 1, 2 | xorbi12i 1477 | . 2 |
4 | hadass 1536 | . 2 hadd | |
5 | hadass 1536 | . 2 hadd | |
6 | 3, 4, 5 | 3bitr4i 292 | 1 hadd hadd |
Colors of variables: wff setvar class |
Syntax hints: 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: hadrot 1540 |
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