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Mirrors > Home > ILE Home > Th. List > foov | Unicode version |
Description: An onto mapping of an operation expressed in terms of operation values. (Contributed by NM, 29-Oct-2006.) |
Ref | Expression |
---|---|
foov |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffo3 5626 | . 2 | |
2 | fveq2 5480 | . . . . . . 7 | |
3 | df-ov 5839 | . . . . . . 7 | |
4 | 2, 3 | eqtr4di 2215 | . . . . . 6 |
5 | 4 | eqeq2d 2176 | . . . . 5 |
6 | 5 | rexxp 4742 | . . . 4 |
7 | 6 | ralbii 2470 | . . 3 |
8 | 7 | anbi2i 453 | . 2 |
9 | 1, 8 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1342 wral 2442 wrex 2443 cop 3573 cxp 4596 wf 5178 wfo 5180 cfv 5182 (class class class)co 5836 |
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-sbc 2947 df-csb 3041 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-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-fo 5188 df-fv 5190 df-ov 5839 |
This theorem is referenced by: (None) |
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