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Mirrors > Home > MPE Home > Th. List > xorass | Structured version Visualization version Unicode version |
Description: The connector is associative. (Contributed by FL, 22-Nov-2010.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) (Proof shortened by Wolf Lammen, 20-Jun-2020.) |
Ref | Expression |
---|---|
xorass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xor3 372 | . . 3 | |
2 | biass 374 | . . . 4 | |
3 | xnor 1466 | . . . . 5 | |
4 | 3 | bibi1i 328 | . . . 4 |
5 | xnor 1466 | . . . . 5 | |
6 | 5 | bibi2i 327 | . . . 4 |
7 | 2, 4, 6 | 3bitr3i 290 | . . 3 |
8 | nbbn 373 | . . 3 | |
9 | 1, 7, 8 | 3bitr2ri 289 | . 2 |
10 | df-xor 1465 | . 2 | |
11 | df-xor 1465 | . 2 | |
12 | 9, 10, 11 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wxo 1464 |
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 |
This theorem is referenced by: hadass 1536 |
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