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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 1521 | . . 3 | |
2 | nfe1 1476 | . . . 4 | |
3 | 2 | nfmo 2026 | . . 3 |
4 | nfa1 1521 | . . . . 5 | |
5 | nfe1 1476 | . . . . . . 7 | |
6 | 5 | nfex 1617 | . . . . . 6 |
7 | 6 | nfmo 2026 | . . . . 5 |
8 | copsexg 4204 | . . . . . . . 8 | |
9 | 8 | mobidv 2042 | . . . . . . 7 |
10 | 9 | biimpcd 158 | . . . . . 6 |
11 | 10 | sps 1517 | . . . . 5 |
12 | 4, 7, 11 | exlimd 1577 | . . . 4 |
13 | 12 | sps 1517 | . . 3 |
14 | 1, 3, 13 | exlimd 1577 | . 2 |
15 | moanimv 2081 | . . 3 | |
16 | simpl 108 | . . . . . 6 | |
17 | 16 | 2eximi 1581 | . . . . 5 |
18 | 17 | ancri 322 | . . . 4 |
19 | 18 | moimi 2071 | . . 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 1333 wceq 1335 wex 1472 wmo 2007 cop 3563 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 |
This theorem is referenced by: mosubop 4652 funoprabg 5920 |
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