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Mirrors > Home > ILE Home > Th. List > xordc1 | Unicode version |
Description: Exclusive or implies the left proposition is decidable. (Contributed by Jim Kingdon, 12-Mar-2018.) |
Ref | Expression |
---|---|
xordc1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | andir 809 |
. . 3
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2 | simpl 108 |
. . . 4
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3 | imnan 680 |
. . . . . 6
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4 | ancom 264 |
. . . . . 6
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5 | 3, 4 | xchbinxr 673 |
. . . . 5
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6 | pm3.35 345 |
. . . . 5
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7 | 5, 6 | sylan2br 286 |
. . . 4
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8 | 2, 7 | orim12i 749 |
. . 3
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9 | 1, 8 | sylbi 120 |
. 2
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10 | df-xor 1355 |
. 2
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11 | df-dc 821 |
. 2
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12 | 9, 10, 11 | 3imtr4i 200 |
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-dc 821 df-xor 1355 |
This theorem is referenced by: (None) |
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