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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 3141 | . . . . 5 | |
2 | 1 | pm4.71rd 392 | . . . 4 |
3 | 2 | anbi1d 462 | . . 3 |
4 | anass 399 | . . 3 | |
5 | 3, 4 | bitrdi 195 | . 2 |
6 | 5 | rexbidv2 2473 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2141 wrex 2449 wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 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-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-rex 2454 df-in 3127 df-ss 3134 |
This theorem is referenced by: 1idprl 7552 1idpru 7553 ltexprlemm 7562 suplocexprlemmu 7680 oddnn02np1 11839 oddge22np1 11840 evennn02n 11841 evennn2n 11842 |
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