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Mirrors > Home > ILE Home > Th. List > xoranor | Unicode version |
Description: One way of defining exclusive or. Equivalent to df-xor 1376. (Contributed by Jim Kingdon and Mario Carneiro, 1-Mar-2018.) |
Ref | Expression |
---|---|
xoranor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1376 |
. . 3
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2 | ax-ia3 108 |
. . . . . . 7
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3 | 2 | con3d 631 |
. . . . . 6
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4 | olc 711 |
. . . . . 6
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5 | 3, 4 | syl6 33 |
. . . . 5
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6 | pm3.21 264 |
. . . . . . 7
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7 | 6 | con3d 631 |
. . . . . 6
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8 | orc 712 |
. . . . . 6
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9 | 7, 8 | syl6 33 |
. . . . 5
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10 | 5, 9 | jaoi 716 |
. . . 4
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11 | 10 | imdistani 445 |
. . 3
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12 | 1, 11 | sylbi 121 |
. 2
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13 | pm3.14 753 |
. . . 4
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14 | 13 | anim2i 342 |
. . 3
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15 | 14, 1 | sylibr 134 |
. 2
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16 | 12, 15 | impbii 126 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-xor 1376 |
This theorem is referenced by: excxor 1378 xoror 1379 |
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