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Mirrors > Home > ILE Home > Th. List > anxordi | Unicode version |
Description: Conjunction distributes over exclusive-or. (Contributed by Mario Carneiro and Jim Kingdon, 7-Oct-2018.) |
Ref | Expression |
---|---|
anxordi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 |
. 2
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2 | df-xor 1355 |
. . . 4
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3 | 2 | simplbi 272 |
. . 3
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4 | simpl 108 |
. . . 4
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5 | simpl 108 |
. . . 4
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6 | 4, 5 | jaoi 706 |
. . 3
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7 | 3, 6 | syl 14 |
. 2
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8 | ibar 299 |
. . 3
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9 | ibar 299 |
. . . 4
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10 | ibar 299 |
. . . 4
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11 | 9, 10 | xorbi12d 1361 |
. . 3
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12 | 8, 11 | bitr3d 189 |
. 2
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13 | 1, 7, 12 | pm5.21nii 694 |
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: rpnegap 9503 |
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