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Mirrors > Home > ILE Home > Th. List > ssiun2 | Unicode version |
Description: Identity law for subset of an indexed union. (Contributed by NM, 12-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
ssiun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspe 2458 | . . . 4 | |
2 | 1 | ex 114 | . . 3 |
3 | eliun 3787 | . . 3 | |
4 | 2, 3 | syl6ibr 161 | . 2 |
5 | 4 | ssrdv 3073 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 wrex 2394 wss 3041 ciun 3783 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-in 3047 df-ss 3054 df-iun 3785 |
This theorem is referenced by: ssiun2s 3827 triun 4009 ixpf 6582 |
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