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Mirrors > Home > ILE Home > Th. List > Mathboxes > decidr | Unicode version |
Description: Sufficient condition for being decidable in another class. (Contributed by BJ, 19-Feb-2022.) |
Ref | Expression |
---|---|
decidr.1 |
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Ref | Expression |
---|---|
decidr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | decidr.1 |
. . . 4
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2 | df-dc 782 |
. . . 4
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3 | 1, 2 | syl6ibr 161 |
. . 3
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4 | 3 | alrimiv 1803 |
. 2
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5 | df-dcin 11998 |
. . 3
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6 | df-ral 2365 |
. . 3
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7 | 5, 6 | bitri 183 |
. 2
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8 | 4, 7 | sylibr 133 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-17 1465 |
This theorem depends on definitions: df-bi 116 df-dc 782 df-ral 2365 df-dcin 11998 |
This theorem is referenced by: decidin 12001 uzdcinzz 12002 sumdc2 12003 |
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