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Mirrors > Home > ILE Home > Th. List > elssabg | Unicode version |
Description: Membership in a class abstraction involving a subset. Unlike elabg 2867, does not have to be a set. (Contributed by NM, 29-Aug-2006.) |
Ref | Expression |
---|---|
elssabg.1 |
Ref | Expression |
---|---|
elssabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssexg 4115 | . . . 4 | |
2 | 1 | expcom 115 | . . 3 |
3 | 2 | adantrd 277 | . 2 |
4 | sseq1 3160 | . . . 4 | |
5 | elssabg.1 | . . . 4 | |
6 | 4, 5 | anbi12d 465 | . . 3 |
7 | 6 | elab3g 2872 | . 2 |
8 | 3, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 cab 2150 cvv 2721 wss 3111 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4094 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 df-ss 3124 |
This theorem is referenced by: (None) |
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