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Mirrors > Home > ILE Home > Th. List > iunss2 | Unicode version |
Description: A subclass condition on the members of two indexed classes and that implies a subclass relation on their indexed unions. Generalization of Proposition 8.6 of [TakeutiZaring] p. 59. Compare uniss2 3803. (Contributed by NM, 9-Dec-2004.) |
Ref | Expression |
---|---|
iunss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssiun 3891 | . . 3 | |
2 | 1 | ralimi 2520 | . 2 |
3 | iunss 3890 | . 2 | |
4 | 2, 3 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wral 2435 wrex 2436 wss 3102 ciun 3849 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 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-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-in 3108 df-ss 3115 df-iun 3851 |
This theorem is referenced by: iunxdif2 3897 rdgss 6330 |
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