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Mirrors > Home > ILE Home > Th. List > rexss | Unicode version |
Description: Restricted existential quantification on a subset in terms of superset. (Contributed by Stefan O'Rear, 3-Apr-2015.) |
Ref | Expression |
---|---|
rexss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3122 | . . . . 5 | |
2 | 1 | pm4.71rd 392 | . . . 4 |
3 | 2 | anbi1d 461 | . . 3 |
4 | anass 399 | . . 3 | |
5 | 3, 4 | bitrdi 195 | . 2 |
6 | 5 | rexbidv2 2460 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2128 wrex 2436 wss 3102 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-rex 2441 df-in 3108 df-ss 3115 |
This theorem is referenced by: 1idprl 7510 1idpru 7511 ltexprlemm 7520 suplocexprlemmu 7638 oddnn02np1 11770 oddge22np1 11771 evennn02n 11772 evennn2n 11773 |
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