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Mirrors > Home > ILE Home > Th. List > mo2icl | Unicode version |
Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.) |
Ref | Expression |
---|---|
mo2icl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1528 | . . . . 5 | |
2 | vex 2724 | . . . . . . . 8 | |
3 | eleq1 2227 | . . . . . . . 8 | |
4 | 2, 3 | mpbii 147 | . . . . . . 7 |
5 | 4 | imim2i 12 | . . . . . 6 |
6 | 5 | sps 1524 | . . . . 5 |
7 | 1, 6 | eximd 1599 | . . . 4 |
8 | 19.9v 1858 | . . . 4 | |
9 | 7, 8 | syl6ib 160 | . . 3 |
10 | eqeq2 2174 | . . . . . . . 8 | |
11 | 10 | imbi2d 229 | . . . . . . 7 |
12 | 11 | albidv 1811 | . . . . . 6 |
13 | 12 | imbi1d 230 | . . . . 5 |
14 | nfv 1515 | . . . . . . 7 | |
15 | 14 | mo2r 2065 | . . . . . 6 |
16 | 15 | 19.23bi 1579 | . . . . 5 |
17 | 13, 16 | vtoclg 2781 | . . . 4 |
18 | 17 | com12 30 | . . 3 |
19 | 9, 18 | syld 45 | . 2 |
20 | moabs 2062 | . 2 | |
21 | 19, 20 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wceq 1342 wex 1479 wmo 2014 wcel 2135 cvv 2721 |
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 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 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 |
This theorem is referenced by: invdisj 3970 |
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