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Mirrors > Home > ILE Home > Th. List > dcbid | Unicode version |
Description: The equivalent of a decidable proposition is decidable. (Contributed by Jim Kingdon, 7-Sep-2019.) |
Ref | Expression |
---|---|
dcbid.1 |
Ref | Expression |
---|---|
dcbid | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcbid.1 | . . 3 | |
2 | 1 | notbid 624 | . . 3 |
3 | 1, 2 | orbi12d 739 | . 2 |
4 | df-dc 776 | . 2 DECID | |
5 | df-dc 776 | . 2 DECID | |
6 | 3, 4, 5 | 3bitr4g 221 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 103 wo 661 DECID wdc 775 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 |
This theorem depends on definitions: df-bi 115 df-dc 776 |
This theorem is referenced by: ltdcpi 6513 enqdc 6551 enqdc1 6552 ltdcnq 6587 exfzdc 9249 dvdsdc 10203 zdvdsdc 10216 zsupcllemstep 10341 infssuzex 10345 |
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