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Mirrors > Home > ILE Home > Th. List > ssralv | Unicode version |
Description: Quantification restricted to a subclass. (Contributed by NM, 11-Mar-2006.) |
Ref | Expression |
---|---|
ssralv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3132 | . . 3 | |
2 | 1 | imim1d 75 | . 2 |
3 | 2 | ralimdv2 2534 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 wral 2442 wss 3112 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-ral 2447 df-in 3118 df-ss 3125 |
This theorem is referenced by: iinss1 3873 poss 4271 sess2 4311 trssord 4353 funco 5223 funimaexglem 5266 isores3 5778 isoini2 5782 smores 6252 smores2 6254 tfrlem5 6274 resixp 6691 ac6sfi 6856 difinfinf 7058 peano5nnnn 7825 peano5nni 8852 caucvgre 10913 rexanuz 10920 cau3lem 11046 isumclim3 11354 fsumiun 11408 pcfac 12269 ctinf 12326 strsetsid 12390 tgcn 12775 tgcnp 12776 cnss2 12794 cncnp 12797 sslm 12814 metrest 13073 rescncf 13135 suplociccex 13170 limcresi 13202 nninfsellemeq 13756 |
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