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Mirrors > Home > ILE Home > Th. List > funres | Unicode version |
Description: A restriction of a function is a function. Compare Exercise 18 of [TakeutiZaring] p. 25. (Contributed by NM, 16-Aug-1994.) |
Ref | Expression |
---|---|
funres |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resss 4813 | . 2 | |
2 | funss 5112 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wss 3041 cres 4511 wfun 5087 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-br 3900 df-opab 3960 df-rel 4516 df-cnv 4517 df-co 4518 df-res 4521 df-fun 5095 |
This theorem is referenced by: fnssresb 5205 fnresi 5210 fores 5324 respreima 5516 resfunexg 5609 funfvima 5617 smores 6157 smores2 6159 frecfun 6260 sbthlem7 6819 setsfun 11921 setsfun0 11922 |
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