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Mirrors > Home > ILE Home > Th. List > elrabsf | Unicode version |
Description: Membership in a restricted class abstraction, expressed with explicit class substitution. (The variation elrabf 2884 has implicit substitution). The hypothesis specifies that must not be a free variable in . (Contributed by NM, 30-Sep-2003.) (Proof shortened by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
elrabsf.1 |
Ref | Expression |
---|---|
elrabsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 2957 | . 2 | |
2 | elrabsf.1 | . . 3 | |
3 | nfcv 2312 | . . 3 | |
4 | nfv 1521 | . . 3 | |
5 | nfsbc1v 2973 | . . 3 | |
6 | sbceq1a 2964 | . . 3 | |
7 | 2, 3, 4, 5, 6 | cbvrab 2728 | . 2 |
8 | 1, 7 | elrab2 2889 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wcel 2141 wnfc 2299 crab 2452 wsbc 2955 |
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-rab 2457 df-v 2732 df-sbc 2956 |
This theorem is referenced by: mpoxopovel 6218 zsupcllemstep 11893 infssuzex 11897 |
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