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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1355 |
. . 3
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2 | imnan 680 |
. . . . 5
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3 | 2 | biimpri 132 |
. . . 4
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4 | 3 | adantl 275 |
. . 3
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5 | 1, 4 | sylbi 120 |
. 2
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6 | pm2.53 712 |
. . . . 5
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7 | 6 | orcoms 720 |
. . . 4
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8 | 7 | adantr 274 |
. . 3
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9 | 1, 8 | sylbi 120 |
. 2
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10 | 5, 9 | impbid 128 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-xor 1355 |
This theorem is referenced by: xornbi 1365 zeo4 11603 odd2np1 11606 |
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