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Mirrors > Home > MPE Home > Th. List > ssiun2 | Structured version Visualization version 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 3003 | . . . 4 | |
2 | 1 | ex 450 | . . 3 |
3 | eliun 4524 | . . 3 | |
4 | 2, 3 | syl6ibr 242 | . 2 |
5 | 4 | ssrdv 3609 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wrex 2913 wss 3574 ciun 4520 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-iun 4522 |
This theorem is referenced by: ssiun2s 4564 disjxiun 4649 disjxiunOLD 4650 triun 4766 iunopeqop 4981 ixpf 7930 ixpiunwdom 8496 r1sdom 8637 r1val1 8649 rankuni2b 8716 rankval4 8730 cplem1 8752 domtriomlem 9264 ac6num 9301 iunfo 9361 iundom2g 9362 pwfseqlem3 9482 inar1 9597 tskuni 9605 iunconnlem 21230 ptclsg 21418 ovoliunlem1 23270 limciun 23658 ssiun2sf 29378 bnj906 31000 bnj999 31027 bnj1014 31030 bnj1408 31104 trpredrec 31738 iunmapss 39407 ssmapsn 39408 sge0iunmpt 40635 sge0iun 40636 voliunsge0lem 40689 omeiunltfirp 40733 |
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