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Mirrors > Home > ILE Home > Th. List > fvoveq1 | Unicode version |
Description: Equality theorem for nested function and operation value. Closed form of fvoveq1d 5861. (Contributed by AV, 23-Jul-2022.) |
Ref | Expression |
---|---|
fvoveq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 | |
2 | 1 | fvoveq1d 5861 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 cfv 5185 (class class class)co 5839 |
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-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2726 df-un 3118 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-br 3980 df-iota 5150 df-fv 5193 df-ov 5842 |
This theorem is referenced by: seq3val 10387 seqvalcd 10388 seqf 10390 seq3p1 10391 seqovcd 10392 seqp1cd 10395 seq3shft2 10402 seq3f1olemqsum 10429 facp1 10637 serf0 11287 fsumrelem 11406 mertenslemub 11469 mertenslemi1 11470 mertenslem2 11471 mertensabs 11472 pcfac 12274 ennnfonelemj0 12328 ennnfonelemjn 12329 ennnfonelem0 12332 ennnfonelemp1 12333 ennnfonelemnn0 12349 nninfdclemcl 12375 nninfdclemp1 12377 nninfdc 12380 comet 13097 mulc1cncf 13174 cncfco 13176 mulcncflem 13188 mulcncf 13189 ivthinclemlopn 13212 ivthinclemuopn 13214 limcimolemlt 13231 limccoap 13245 eflt 13294 rpcxpef 13413 |
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