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Mirrors > Home > ILE Home > Th. List > morex | Unicode version |
Description: Derive membership from uniqueness. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
morex.1 | |
morex.2 |
Ref | Expression |
---|---|
morex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2420 | . . . 4 | |
2 | exancom 1587 | . . . 4 | |
3 | 1, 2 | bitri 183 | . . 3 |
4 | nfmo1 2009 | . . . . . 6 | |
5 | nfe1 1472 | . . . . . 6 | |
6 | 4, 5 | nfan 1544 | . . . . 5 |
7 | mopick 2075 | . . . . 5 | |
8 | 6, 7 | alrimi 1502 | . . . 4 |
9 | morex.1 | . . . . 5 | |
10 | morex.2 | . . . . . 6 | |
11 | eleq1 2200 | . . . . . 6 | |
12 | 10, 11 | imbi12d 233 | . . . . 5 |
13 | 9, 12 | spcv 2774 | . . . 4 |
14 | 8, 13 | syl 14 | . . 3 |
15 | 3, 14 | sylan2b 285 | . 2 |
16 | 15 | ancoms 266 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 wmo 1998 wrex 2415 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-rex 2420 df-v 2683 |
This theorem is referenced by: (None) |
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