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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 2354 | . 2 | |
2 | nfsab1 2071 | . . . 4 | |
3 | nfv 1461 | . . . 4 | |
4 | 2, 3 | nfan 1497 | . . 3 |
5 | nfv 1461 | . . 3 | |
6 | eleq1 2141 | . . . . 5 | |
7 | abid 2069 | . . . . 5 | |
8 | 6, 7 | syl6bb 194 | . . . 4 |
9 | ralab2.1 | . . . 4 | |
10 | 8, 9 | anbi12d 456 | . . 3 |
11 | 4, 5, 10 | cbvex 1679 | . 2 |
12 | 1, 11 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wex 1421 wcel 1433 cab 2067 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-rex 2354 |
This theorem is referenced by: rexrab2 2759 |
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