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Mirrors > Home > ILE Home > Th. List > ffnov | Unicode version |
Description: An operation maps to a class to which all values belong. (Contributed by NM, 7-Feb-2004.) |
Ref | Expression |
---|---|
ffnov |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffnfv 5625 | . 2 | |
2 | fveq2 5468 | . . . . . 6 | |
3 | df-ov 5827 | . . . . . 6 | |
4 | 2, 3 | eqtr4di 2208 | . . . . 5 |
5 | 4 | eleq1d 2226 | . . . 4 |
6 | 5 | ralxp 4729 | . . 3 |
7 | 6 | anbi2i 453 | . 2 |
8 | 1, 7 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wcel 2128 wral 2435 cop 3563 cxp 4584 wfn 5165 wf 5166 cfv 5170 (class class class)co 5824 |
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-csb 3032 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-iun 3851 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-f 5174 df-fv 5178 df-ov 5827 |
This theorem is referenced by: fovcl 5926 axaddf 7788 axmulf 7789 txdis1cn 12689 isxmet2d 12759 xmetresbl 12851 comet 12910 tgqioo 12958 |
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