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Mirrors > Home > ILE Home > Th. List > elabrex | Unicode version |
Description: Elementhood in an image set. (Contributed by Mario Carneiro, 14-Jan-2014.) |
Ref | Expression |
---|---|
elabrex.1 |
Ref | Expression |
---|---|
elabrex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1352 | . . . 4 | |
2 | csbeq1a 3058 | . . . . . . 7 | |
3 | 2 | equcoms 1701 | . . . . . 6 |
4 | a1tru 1364 | . . . . . 6 | |
5 | 3, 4 | 2thd 174 | . . . . 5 |
6 | 5 | rspcev 2834 | . . . 4 |
7 | 1, 6 | mpan2 423 | . . 3 |
8 | elabrex.1 | . . . 4 | |
9 | eqeq1 2177 | . . . . 5 | |
10 | 9 | rexbidv 2471 | . . . 4 |
11 | 8, 10 | elab 2874 | . . 3 |
12 | 7, 11 | sylibr 133 | . 2 |
13 | nfv 1521 | . . . 4 | |
14 | nfcsb1v 3082 | . . . . 5 | |
15 | 14 | nfeq2 2324 | . . . 4 |
16 | 2 | eqeq2d 2182 | . . . 4 |
17 | 13, 15, 16 | cbvrex 2693 | . . 3 |
18 | 17 | abbii 2286 | . 2 |
19 | 12, 18 | eleqtrrdi 2264 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wtru 1349 wcel 2141 cab 2156 wrex 2449 cvv 2730 csb 3049 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 |
This theorem is referenced by: eusvobj2 5836 |
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