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Mirrors > Home > ILE Home > Th. List > fvssunirng | Unicode version |
Description: The result of a function value is always a subset of the union of the range, if the input is a set. (Contributed by Stefan O'Rear, 2-Nov-2014.) (Revised by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
fvssunirng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2724 | . . . . 5 | |
2 | brelrng 4829 | . . . . . 6 | |
3 | 2 | 3exp 1191 | . . . . 5 |
4 | 1, 3 | mpi 15 | . . . 4 |
5 | elssuni 3811 | . . . 4 | |
6 | 4, 5 | syl6 33 | . . 3 |
7 | 6 | alrimiv 1861 | . 2 |
8 | fvss 5494 | . 2 | |
9 | 7, 8 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wcel 2135 cvv 2721 wss 3111 cuni 3783 class class class wbr 3976 crn 4599 cfv 5182 |
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-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-cnv 4606 df-dm 4608 df-rn 4609 df-iota 5147 df-fv 5190 |
This theorem is referenced by: fvexg 5499 strfvssn 12359 xmetunirn 12905 mopnval 12989 |
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