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Mirrors > Home > ILE Home > Th. List > elrnrexdmb | Unicode version |
Description: For any element in the range of a function there is an element in the domain of the function for which the function value is the element of the range. (Contributed by Alexander van der Vekens, 17-Dec-2017.) |
Ref | Expression |
---|---|
elrnrexdmb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 5200 | . . 3 | |
2 | fvelrnb 5516 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 |
4 | eqcom 2159 | . . 3 | |
5 | 4 | rexbii 2464 | . 2 |
6 | 3, 5 | bitr4di 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wcel 2128 wrex 2436 cdm 4586 crn 4587 wfun 5164 wfn 5165 cfv 5170 |
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 4082 ax-pow 4135 ax-pr 4169 |
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-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-mpt 4027 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-iota 5135 df-fun 5172 df-fn 5173 df-fv 5178 |
This theorem is referenced by: (None) |
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