Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mosubopt | Unicode version |
Description: "At most one" remains true inside ordered pair quantification. (Contributed by NM, 28-Aug-2007.) |
Ref | Expression |
---|---|
mosubopt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1506 | . . 3 | |
2 | nfe1 1457 | . . . 4 | |
3 | 2 | nfmo 1997 | . . 3 |
4 | nfa1 1506 | . . . . 5 | |
5 | nfe1 1457 | . . . . . . 7 | |
6 | 5 | nfex 1601 | . . . . . 6 |
7 | 6 | nfmo 1997 | . . . . 5 |
8 | copsexg 4136 | . . . . . . . 8 | |
9 | 8 | mobidv 2013 | . . . . . . 7 |
10 | 9 | biimpcd 158 | . . . . . 6 |
11 | 10 | sps 1502 | . . . . 5 |
12 | 4, 7, 11 | exlimd 1561 | . . . 4 |
13 | 12 | sps 1502 | . . 3 |
14 | 1, 3, 13 | exlimd 1561 | . 2 |
15 | moanimv 2052 | . . 3 | |
16 | simpl 108 | . . . . . 6 | |
17 | 16 | 2eximi 1565 | . . . . 5 |
18 | 17 | ancri 322 | . . . 4 |
19 | 18 | moimi 2042 | . . 3 |
20 | 15, 19 | sylbir 134 | . 2 |
21 | 14, 20 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1314 wceq 1316 wex 1453 wmo 1978 cop 3500 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 |
This theorem is referenced by: mosubop 4575 funoprabg 5838 |
Copyright terms: Public domain | W3C validator |