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Mirrors > Home > ILE Home > Th. List > rexab2 | Unicode version |
Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
ralab2.1 |
Ref | Expression |
---|---|
rexab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2422 | . 2 | |
2 | nfsab1 2129 | . . . 4 | |
3 | nfv 1508 | . . . 4 | |
4 | 2, 3 | nfan 1544 | . . 3 |
5 | nfv 1508 | . . 3 | |
6 | eleq1 2202 | . . . . 5 | |
7 | abid 2127 | . . . . 5 | |
8 | 6, 7 | syl6bb 195 | . . . 4 |
9 | ralab2.1 | . . . 4 | |
10 | 8, 9 | anbi12d 464 | . . 3 |
11 | 4, 5, 10 | cbvex 1729 | . 2 |
12 | 1, 11 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wex 1468 wcel 1480 cab 2125 wrex 2417 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-rex 2422 |
This theorem is referenced by: rexrab2 2851 |
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