Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elabgt | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 2825.) (Contributed by NM, 7-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
elabgt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abid 2125 | . . . . . . 7 | |
2 | eleq1 2200 | . . . . . . 7 | |
3 | 1, 2 | syl5bbr 193 | . . . . . 6 |
4 | 3 | bibi1d 232 | . . . . 5 |
5 | 4 | biimpd 143 | . . . 4 |
6 | 5 | a2i 11 | . . 3 |
7 | 6 | alimi 1431 | . 2 |
8 | nfcv 2279 | . . . 4 | |
9 | nfab1 2281 | . . . . . 6 | |
10 | 9 | nfel2 2292 | . . . . 5 |
11 | nfv 1508 | . . . . 5 | |
12 | 10, 11 | nfbi 1568 | . . . 4 |
13 | pm5.5 241 | . . . 4 | |
14 | 8, 12, 13 | spcgf 2763 | . . 3 |
15 | 14 | imp 123 | . 2 |
16 | 7, 15 | sylan2 284 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wcel 1480 cab 2123 |
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-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 |
This theorem is referenced by: elrab3t 2834 |
Copyright terms: Public domain | W3C validator |