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Mirrors > Home > ILE Home > Th. List > r19.30dc | Unicode version |
Description: Restricted quantifier version of 19.30dc 1607. (Contributed by Scott Fenton, 25-Feb-2011.) (Proof shortened by Wolf Lammen, 18-Jun-2023.) |
Ref | Expression |
---|---|
r19.30dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralnex 2445 | . . . . 5 | |
2 | pm2.53 712 | . . . . . . 7 | |
3 | 2 | orcoms 720 | . . . . . 6 |
4 | 3 | ral2imi 2522 | . . . . 5 |
5 | 1, 4 | syl5bir 152 | . . . 4 |
6 | 5 | adantr 274 | . . 3 DECID |
7 | dfordc 878 | . . . 4 DECID | |
8 | 7 | adantl 275 | . . 3 DECID |
9 | 6, 8 | mpbird 166 | . 2 DECID |
10 | 9 | orcomd 719 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 DECID wdc 820 wral 2435 wrex 2436 |
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 1427 ax-gen 1429 ax-ie2 1474 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1338 df-fal 1341 df-ral 2440 df-rex 2441 |
This theorem is referenced by: exmidontriimlem1 7157 |
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