Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rabsnt | Unicode version |
Description: Truth implied by equality of a restricted class abstraction and a singleton. (Contributed by NM, 29-May-2006.) (Proof shortened by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
rabsnt.1 | |
rabsnt.2 |
Ref | Expression |
---|---|
rabsnt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabsnt.1 | . . . 4 | |
2 | 1 | snid 3526 | . . 3 |
3 | id 19 | . . 3 | |
4 | 2, 3 | eleqtrrid 2207 | . 2 |
5 | rabsnt.2 | . . . 4 | |
6 | 5 | elrab 2813 | . . 3 |
7 | 6 | simprbi 273 | . 2 |
8 | 4, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 crab 2397 cvv 2660 csn 3497 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-sn 3503 |
This theorem is referenced by: ontr2exmid 4410 onsucsssucexmid 4412 ordsoexmid 4447 unfiexmid 6774 |
Copyright terms: Public domain | W3C validator |