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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 1521 | . . . . 5 | |
2 | vex 2684 | . . . . . . . 8 | |
3 | eleq1 2200 | . . . . . . . 8 | |
4 | 2, 3 | mpbii 147 | . . . . . . 7 |
5 | 4 | imim2i 12 | . . . . . 6 |
6 | 5 | sps 1517 | . . . . 5 |
7 | 1, 6 | eximd 1591 | . . . 4 |
8 | 19.9v 1843 | . . . 4 | |
9 | 7, 8 | syl6ib 160 | . . 3 |
10 | eqeq2 2147 | . . . . . . . 8 | |
11 | 10 | imbi2d 229 | . . . . . . 7 |
12 | 11 | albidv 1796 | . . . . . 6 |
13 | 12 | imbi1d 230 | . . . . 5 |
14 | nfv 1508 | . . . . . . 7 | |
15 | 14 | mo2r 2049 | . . . . . 6 |
16 | 15 | 19.23bi 1571 | . . . . 5 |
17 | 13, 16 | vtoclg 2741 | . . . 4 |
18 | 17 | com12 30 | . . 3 |
19 | 9, 18 | syld 45 | . 2 |
20 | moabs 2046 | . 2 | |
21 | 19, 20 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 wex 1468 wcel 1480 wmo 1998 cvv 2681 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 |
This theorem is referenced by: invdisj 3918 |
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