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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 1307 | . . 3 | |
2 | imnan 656 | . . . . 5 | |
3 | 2 | biimpri 131 | . . . 4 |
4 | 3 | adantl 271 | . . 3 |
5 | 1, 4 | sylbi 119 | . 2 |
6 | pm2.53 673 | . . . . 5 | |
7 | 6 | orcoms 681 | . . . 4 |
8 | 7 | adantr 270 | . . 3 |
9 | 1, 8 | sylbi 119 | . 2 |
10 | 5, 9 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wo 661 wxo 1306 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 |
This theorem depends on definitions: df-bi 115 df-xor 1307 |
This theorem is referenced by: xornbi 1317 zeo4 10269 odd2np1 10272 |
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