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Mirrors > Home > NFE 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 3922. (Contributed by NM, 9-Dec-2004.) |
Ref | Expression |
---|---|
iunss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssiun 4008 | . . 3 | |
2 | 1 | ralimi 2689 | . 2 |
3 | iunss 4007 | . 2 | |
4 | 2, 3 | sylibr 203 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wral 2614 wrex 2615 wss 3257 ciun 3969 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-iun 3971 |
This theorem is referenced by: iunxdif2 4014 |
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