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Mirrors > Home > ILE Home > Th. List > ssres2 | Unicode version |
Description: Subclass theorem for restriction. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
ssres2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpss1 4708 | . . 3 | |
2 | sslin 3343 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-res 4610 | . 2 | |
5 | df-res 4610 | . 2 | |
6 | 3, 4, 5 | 3sstr4g 3180 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 cvv 2721 cin 3110 wss 3111 cxp 4596 cres 4600 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 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-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 df-ss 3124 df-opab 4038 df-xp 4604 df-res 4610 |
This theorem is referenced by: imass2 4974 resasplitss 5361 fnsnsplitss 5678 1stcof 6123 2ndcof 6124 |
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