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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 1534 | . . 3 | |
2 | nfe1 1489 | . . . 4 | |
3 | 2 | nfmo 2039 | . . 3 |
4 | nfa1 1534 | . . . . 5 | |
5 | nfe1 1489 | . . . . . . 7 | |
6 | 5 | nfex 1630 | . . . . . 6 |
7 | 6 | nfmo 2039 | . . . . 5 |
8 | copsexg 4229 | . . . . . . . 8 | |
9 | 8 | mobidv 2055 | . . . . . . 7 |
10 | 9 | biimpcd 158 | . . . . . 6 |
11 | 10 | sps 1530 | . . . . 5 |
12 | 4, 7, 11 | exlimd 1590 | . . . 4 |
13 | 12 | sps 1530 | . . 3 |
14 | 1, 3, 13 | exlimd 1590 | . 2 |
15 | moanimv 2094 | . . 3 | |
16 | simpl 108 | . . . . . 6 | |
17 | 16 | 2eximi 1594 | . . . . 5 |
18 | 17 | ancri 322 | . . . 4 |
19 | 18 | moimi 2084 | . . 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 1346 wceq 1348 wex 1485 wmo 2020 cop 3586 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 |
This theorem is referenced by: mosubop 4677 funoprabg 5952 |
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