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Mirrors > Home > ILE Home > Th. List > fnotovb | Unicode version |
Description: Equivalence of operation value and ordered triple membership, analogous to fnopfvb 5549. (Contributed by NM, 17-Dec-2008.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
fnotovb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4652 | . . . 4 | |
2 | fnopfvb 5549 | . . . 4 | |
3 | 1, 2 | sylan2 286 | . . 3 |
4 | 3 | 3impb 1199 | . 2 |
5 | df-ov 5868 | . . 3 | |
6 | 5 | eqeq1i 2183 | . 2 |
7 | df-ot 3599 | . . 3 | |
8 | 7 | eleq1i 2241 | . 2 |
9 | 4, 6, 8 | 3bitr4g 223 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 wb 105 w3a 978 wceq 1353 wcel 2146 cop 3592 cotp 3593 cxp 4618 wfn 5203 cfv 5208 (class class class)co 5865 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-14 2149 ax-ext 2157 ax-sep 4116 ax-pow 4169 ax-pr 4203 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ral 2458 df-rex 2459 df-v 2737 df-sbc 2961 df-un 3131 df-in 3133 df-ss 3140 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-ot 3599 df-uni 3806 df-br 3999 df-opab 4060 df-id 4287 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-iota 5170 df-fun 5210 df-fn 5211 df-fv 5216 df-ov 5868 |
This theorem is referenced by: (None) |
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