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Mirrors > Home > ILE Home > Th. List > elrnmpog | Unicode version |
Description: Membership in the range of an operation class abstraction. (Contributed by NM, 27-Aug-2007.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
rngop.1 |
Ref | Expression |
---|---|
elrnmpog |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2164 | . . 3 | |
2 | 1 | 2rexbidv 2482 | . 2 |
3 | rngop.1 | . . 3 | |
4 | 3 | rnmpo 5933 | . 2 |
5 | 2, 4 | elab2g 2859 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wcel 2128 wrex 2436 crn 4589 cmpo 5828 |
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-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-br 3968 df-opab 4028 df-cnv 4596 df-dm 4598 df-rn 4599 df-oprab 5830 df-mpo 5831 |
This theorem is referenced by: txopn 12735 xmettxlem 12979 xmettx 12980 |
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