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Mirrors > Home > ILE Home > Th. List > oveqan12d | Unicode version |
Description: Equality deduction for operation value. (Contributed by NM, 10-Aug-1995.) |
Ref | Expression |
---|---|
oveq1d.1 | |
opreqan12i.2 |
Ref | Expression |
---|---|
oveqan12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1d.1 | . 2 | |
2 | opreqan12i.2 | . 2 | |
3 | oveq12 5783 | . 2 | |
4 | 1, 2, 3 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 (class class class)co 5774 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: oveqan12rd 5794 offval 5989 offval3 6032 ecovdi 6540 ecovidi 6541 distrpig 7141 addcmpblnq 7175 addpipqqs 7178 mulpipq 7180 addcomnqg 7189 addcmpblnq0 7251 distrnq0 7267 recexprlem1ssl 7441 recexprlem1ssu 7442 1idsr 7576 addcnsrec 7650 mulcnsrec 7651 mulid1 7763 mulsub 8163 mulsub2 8164 muleqadd 8429 divmuldivap 8472 div2subap 8596 addltmul 8956 xnegdi 9651 fzsubel 9840 fzoval 9925 mulexp 10332 sqdivap 10357 crim 10630 readd 10641 remullem 10643 imadd 10649 cjadd 10656 cjreim 10675 sqrtmul 10807 sqabsadd 10827 sqabssub 10828 absmul 10841 abs2dif 10878 binom 11253 sinadd 11443 cosadd 11444 dvds2ln 11526 absmulgcd 11705 gcddiv 11707 bezoutr1 11721 lcmgcd 11759 nn0gcdsq 11878 crth 11900 xmetxp 12676 xmetxpbl 12677 txmetcnp 12687 divcnap 12724 rescncf 12737 |
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