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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 5845 | . 2 | |
4 | 1, 2, 3 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 (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: oveqan12rd 5856 offval 6051 offval3 6094 ecovdi 6603 ecovidi 6604 distrpig 7265 addcmpblnq 7299 addpipqqs 7302 mulpipq 7304 addcomnqg 7313 addcmpblnq0 7375 distrnq0 7391 recexprlem1ssl 7565 recexprlem1ssu 7566 1idsr 7700 addcnsrec 7774 mulcnsrec 7775 mulid1 7887 mulsub 8290 mulsub2 8291 muleqadd 8556 divmuldivap 8599 div2subap 8724 addltmul 9084 xnegdi 9795 fzsubel 9985 fzoval 10073 mulexp 10484 sqdivap 10509 crim 10786 readd 10797 remullem 10799 imadd 10805 cjadd 10812 cjreim 10831 sqrtmul 10963 sqabsadd 10983 sqabssub 10984 absmul 10997 abs2dif 11034 binom 11411 sinadd 11663 cosadd 11664 dvds2ln 11750 absmulgcd 11935 gcddiv 11937 bezoutr1 11951 lcmgcd 11989 nn0gcdsq 12111 crth 12135 pythagtriplem1 12176 pcqmul 12214 xmetxp 13054 xmetxpbl 13055 txmetcnp 13065 divcnap 13102 rescncf 13115 relogoprlem 13336 |
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