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Mirrors > Home > ILE Home > Th. List > fvoveq1d | Unicode version |
Description: Equality deduction for nested function and operation value. (Contributed by AV, 23-Jul-2022.) |
Ref | Expression |
---|---|
fvoveq1d.1 |
Ref | Expression |
---|---|
fvoveq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvoveq1d.1 | . . 3 | |
2 | 1 | oveq1d 5851 | . 2 |
3 | 2 | fveq2d 5484 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 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-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 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 |
This theorem is referenced by: fvoveq1 5859 imbrov2fvoveq 5861 seqvalcd 10384 mulc1cncf 13117 mulcncflem 13131 mulcncf 13132 limccl 13169 ellimc3apf 13170 limcdifap 13172 limcmpted 13173 limcresi 13176 limccoap 13188 dveflem 13228 |
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