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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 1474 | . . . . 5 | |
2 | vex 2604 | . . . . . . . 8 | |
3 | eleq1 2141 | . . . . . . . 8 | |
4 | 2, 3 | mpbii 146 | . . . . . . 7 |
5 | 4 | imim2i 12 | . . . . . 6 |
6 | 5 | sps 1470 | . . . . 5 |
7 | 1, 6 | eximd 1543 | . . . 4 |
8 | 19.9v 1792 | . . . 4 | |
9 | 7, 8 | syl6ib 159 | . . 3 |
10 | eqeq2 2090 | . . . . . . . 8 | |
11 | 10 | imbi2d 228 | . . . . . . 7 |
12 | 11 | albidv 1745 | . . . . . 6 |
13 | 12 | imbi1d 229 | . . . . 5 |
14 | nfv 1461 | . . . . . . 7 | |
15 | 14 | mo2r 1993 | . . . . . 6 |
16 | 15 | 19.23bi 1523 | . . . . 5 |
17 | 13, 16 | vtoclg 2658 | . . . 4 |
18 | 17 | com12 30 | . . 3 |
19 | 9, 18 | syld 44 | . 2 |
20 | moabs 1990 | . 2 | |
21 | 19, 20 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1282 wceq 1284 wex 1421 wcel 1433 wmo 1942 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 |
This theorem is referenced by: invdisj 3780 |
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