Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2reuswapdc | Unicode version |
Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Thierry Arnoux, 7-Apr-2017.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
2reuswapdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2450 | . . 3 | |
2 | 1 | ralbii 2470 | . 2 |
3 | df-ral 2447 | . . . 4 | |
4 | moanimv 2088 | . . . . 5 | |
5 | 4 | albii 1457 | . . . 4 |
6 | 3, 5 | bitr4i 186 | . . 3 |
7 | df-reu 2449 | . . . . . 6 | |
8 | r19.42v 2621 | . . . . . . . . 9 | |
9 | df-rex 2448 | . . . . . . . . 9 | |
10 | 8, 9 | bitr3i 185 | . . . . . . . 8 |
11 | an12 551 | . . . . . . . . 9 | |
12 | 11 | exbii 1592 | . . . . . . . 8 |
13 | 10, 12 | bitri 183 | . . . . . . 7 |
14 | 13 | eubii 2022 | . . . . . 6 |
15 | 7, 14 | bitri 183 | . . . . 5 |
16 | 2euswapdc 2104 | . . . . 5 DECID | |
17 | 15, 16 | syl7bi 164 | . . . 4 DECID |
18 | df-reu 2449 | . . . . . 6 | |
19 | r19.42v 2621 | . . . . . . . 8 | |
20 | df-rex 2448 | . . . . . . . 8 | |
21 | 19, 20 | bitr3i 185 | . . . . . . 7 |
22 | 21 | eubii 2022 | . . . . . 6 |
23 | 18, 22 | bitri 183 | . . . . 5 |
24 | 23 | imbi2i 225 | . . . 4 |
25 | 17, 24 | syl6ibr 161 | . . 3 DECID |
26 | 6, 25 | syl5bi 151 | . 2 DECID |
27 | 2, 26 | syl5bi 151 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 DECID wdc 824 wal 1340 wex 1479 weu 2013 wmo 2014 wcel 2135 wral 2442 wrex 2443 wreu 2444 wrmo 2445 |
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-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-ral 2447 df-rex 2448 df-reu 2449 df-rmo 2450 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |