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Mirrors > Home > ILE Home > Th. List > 19.30dc | Unicode version |
Description: Theorem 19.30 of [Margaris] p. 90, with an additional decidability condition. (Contributed by Jim Kingdon, 21-Jul-2018.) |
Ref | Expression |
---|---|
19.30dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 825 | . 2 DECID | |
2 | olc 701 | . . . 4 | |
3 | 2 | a1d 22 | . . 3 |
4 | alnex 1486 | . . . . 5 | |
5 | orel2 716 | . . . . . 6 | |
6 | 5 | al2imi 1445 | . . . . 5 |
7 | 4, 6 | sylbir 134 | . . . 4 |
8 | orc 702 | . . . 4 | |
9 | 7, 8 | syl6 33 | . . 3 |
10 | 3, 9 | jaoi 706 | . 2 |
11 | 1, 10 | sylbi 120 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 698 DECID wdc 824 wal 1340 wex 1479 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-gen 1436 ax-ie2 1481 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-tru 1345 df-fal 1348 |
This theorem is referenced by: (None) |
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