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Mirrors > Home > ILE Home > Th. List > pm2.61ddc | Unicode version |
Description: Deduction eliminating a decidable antecedent. (Contributed by Jim Kingdon, 4-May-2018.) |
Ref | Expression |
---|---|
pm2.61ddc.1 | |
pm2.61ddc.2 |
Ref | Expression |
---|---|
pm2.61ddc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 743 | . 2 DECID | |
2 | pm2.61ddc.1 | . . . 4 | |
3 | 2 | com12 27 | . . 3 |
4 | pm2.61ddc.2 | . . . 4 | |
5 | 4 | com12 27 | . . 3 |
6 | 3, 5 | jaoi 636 | . 2 |
7 | 1, 6 | sylbi 114 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 629 DECID wdc 742 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 |
This theorem is referenced by: bijadc 776 |
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