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Mirrors > Home > ILE Home > Th. List > fveq1d | Unicode version |
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
fveq1d.1 |
Ref | Expression |
---|---|
fveq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1d.1 | . 2 | |
2 | fveq1 5413 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cfv 5118 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 |
This theorem is referenced by: fveq12d 5421 funssfv 5440 csbfv2g 5451 fvco4 5486 fvmptd 5495 fvmpt2d 5500 mpteqb 5504 fvmptt 5505 fmptco 5579 fvunsng 5607 fvsng 5609 fsnunfv 5614 f1ocnvfv1 5671 f1ocnvfv2 5672 fcof1 5677 fcofo 5678 ofvalg 5984 offval2 5990 ofrfval2 5991 caofinvl 5997 tfrlemi1 6222 rdg0g 6278 freceq1 6282 oav 6343 omv 6344 oeiv 6345 mapxpen 6735 xpmapenlem 6736 exmidomni 7007 fseq1p1m1 9867 seqeq3 10216 seq3f1olemqsum 10266 seq3f1olemstep 10267 seq3f1olemp 10268 seq3id 10274 seq3z 10277 exp3val 10288 bcval5 10502 bcn2 10503 seq3coll 10578 shftcan1 10599 shftcan2 10600 shftvalg 10601 shftval4g 10602 climshft2 11068 sumeq2 11121 summodc 11145 zsumdc 11146 fsum3 11149 isumz 11151 fisumss 11154 fsum3cvg2 11156 isumsplit 11253 prodeq2w 11318 prodeq2 11319 fvsetsid 11982 setsslid 11998 setsslnid 11999 ntrval 12268 clsval 12269 neival 12301 cnpval 12356 txmetcnp 12676 metcnpd 12678 limccl 12786 ellimc3apf 12787 cnplimclemr 12796 limccnp2cntop 12804 dvfvalap 12808 dvfre 12832 peano4nninf 13189 |
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