Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2448 | . . . 4 | |
2 | exancom 1595 | . . . 4 | |
3 | 1, 2 | bitri 183 | . . 3 |
4 | nfmo1 2025 | . . . . . 6 | |
5 | nfe1 1483 | . . . . . 6 | |
6 | 4, 5 | nfan 1552 | . . . . 5 |
7 | mopick 2091 | . . . . 5 | |
8 | 6, 7 | alrimi 1509 | . . . 4 |
9 | morex.1 | . . . . 5 | |
10 | morex.2 | . . . . . 6 | |
11 | eleq1 2227 | . . . . . 6 | |
12 | 10, 11 | imbi12d 233 | . . . . 5 |
13 | 9, 12 | spcv 2815 | . . . 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 1340 wceq 1342 wex 1479 wmo 2014 wcel 2135 wrex 2443 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-rex 2448 df-v 2723 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |