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Mirrors > Home > ILE Home > Th. List > relfvssunirn | Unicode version |
Description: The result of a function value is always a subset of the union of the range, even if it is invalid and thus empty. (Contributed by Stefan O'Rear, 2-Nov-2014.) (Revised by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
relfvssunirn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relelrn 4824 | . . . . 5 | |
2 | 1 | ex 114 | . . . 4 |
3 | elssuni 3802 | . . . 4 | |
4 | 2, 3 | syl6 33 | . . 3 |
5 | 4 | alrimiv 1854 | . 2 |
6 | fvss 5484 | . 2 | |
7 | 5, 6 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1333 wcel 2128 wss 3102 cuni 3774 class class class wbr 3967 crn 4589 wrel 4593 cfv 5172 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-xp 4594 df-rel 4595 df-cnv 4596 df-dm 4598 df-rn 4599 df-iota 5137 df-fv 5180 |
This theorem is referenced by: relrnfvex 5488 |
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