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Mirrors > Home > ILE Home > Th. List > dcbi | Unicode version |
Description: An equivalence of two decidable propositions is decidable. (Contributed by Jim Kingdon, 12-Apr-2018.) |
Ref | Expression |
---|---|
dcbi | DECID DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcim 826 | . . 3 DECID DECID DECID | |
2 | dcim 826 | . . . 4 DECID DECID DECID | |
3 | 2 | com12 30 | . . 3 DECID DECID DECID |
4 | dcan 918 | . . 3 DECID DECID DECID | |
5 | 1, 3, 4 | syl6c 66 | . 2 DECID DECID DECID |
6 | dfbi2 385 | . . 3 | |
7 | 6 | dcbii 825 | . 2 DECID DECID |
8 | 5, 7 | syl6ibr 161 | 1 DECID DECID DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 DECID wdc 819 |
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 603 ax-in2 604 ax-io 698 |
This theorem depends on definitions: df-bi 116 df-dc 820 |
This theorem is referenced by: xor3dc 1365 pm5.15dc 1367 bilukdc 1374 xordidc 1377 |
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