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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 |
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funres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resss 4737 |
. 2
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2 | funss 5034 |
. 2
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3 | 1, 2 | ax-mp 7 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-in 3005 df-ss 3012 df-br 3846 df-opab 3900 df-rel 4445 df-cnv 4446 df-co 4447 df-res 4450 df-fun 5017 |
This theorem is referenced by: fnssresb 5126 fnresi 5131 fores 5242 respreima 5427 resfunexg 5518 funfvima 5526 smores 6057 smores2 6059 frecfun 6160 sbthlem7 6672 setsfun 11529 setsfun0 11530 |
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