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Mirrors > Home > ILE Home > Th. List > xorbin | Unicode version |
Description: A consequence of exclusive or. In classical logic the converse also holds. (Contributed by Jim Kingdon, 8-Mar-2018.) |
Ref | Expression |
---|---|
xorbin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1371 | . . 3 | |
2 | imnan 685 | . . . . 5 | |
3 | 2 | biimpri 132 | . . . 4 |
4 | 3 | adantl 275 | . . 3 |
5 | 1, 4 | sylbi 120 | . 2 |
6 | pm2.53 717 | . . . . 5 | |
7 | 6 | orcoms 725 | . . . 4 |
8 | 7 | adantr 274 | . . 3 |
9 | 1, 8 | sylbi 120 | . 2 |
10 | 5, 9 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 703 wxo 1370 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 |
This theorem depends on definitions: df-bi 116 df-xor 1371 |
This theorem is referenced by: xornbi 1381 zeo4 11822 odd2np1 11825 |
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