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Mirrors > Home > ILE Home > Th. List > dcbid | Unicode version |
Description: Equivalence property for decidability. Deduction form. (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 656 | . . 3 |
3 | 1, 2 | orbi12d 782 | . 2 |
4 | df-dc 820 | . 2 DECID | |
5 | df-dc 820 | . 2 DECID | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 697 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: dcbiit 824 exmidexmid 4120 exmidel 4128 dcdifsnid 6400 finexdc 6796 undifdcss 6811 ssfirab 6822 fidcenumlemrks 6841 difinfsnlem 6984 difinfsn 6985 ctssdclemn0 6995 ctssdccl 6996 ctssdclemr 6997 ctssdc 6998 ltdcpi 7131 enqdc 7169 enqdc1 7170 ltdcnq 7205 fzodcel 9929 exfzdc 10017 sumeq1 11124 sumdc 11127 summodclem2 11151 summodc 11152 zsumdc 11153 fsum3 11156 isumz 11158 isumss 11160 fisumss 11161 isumss2 11162 fsum3cvg2 11163 fsumsersdc 11164 fsumsplit 11176 prodeq1f 11321 prodmodclem2a 11345 prodmodclem2 11346 prodmodc 11347 dvdsdc 11501 zdvdsdc 11514 zsupcllemstep 11638 infssuzex 11642 hashdvds 11897 ennnfonelemr 11936 ennnfonelemim 11937 ctinf 11943 ctiunctlemudc 11950 ctiunct 11953 sumdc2 13006 nninfsellemdc 13206 |
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