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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 5859 | . 2 | |
4 | 1, 2, 3 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 (class class class)co 5850 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5853 |
This theorem is referenced by: oveqan12rd 5870 offval 6065 offval3 6110 ecovdi 6620 ecovidi 6621 distrpig 7282 addcmpblnq 7316 addpipqqs 7319 mulpipq 7321 addcomnqg 7330 addcmpblnq0 7392 distrnq0 7408 recexprlem1ssl 7582 recexprlem1ssu 7583 1idsr 7717 addcnsrec 7791 mulcnsrec 7792 mulid1 7904 mulsub 8307 mulsub2 8308 muleqadd 8573 divmuldivap 8616 div2subap 8741 addltmul 9101 xnegdi 9812 fzsubel 10003 fzoval 10091 mulexp 10502 sqdivap 10527 crim 10809 readd 10820 remullem 10822 imadd 10828 cjadd 10835 cjreim 10854 sqrtmul 10986 sqabsadd 11006 sqabssub 11007 absmul 11020 abs2dif 11057 binom 11434 sinadd 11686 cosadd 11687 dvds2ln 11773 absmulgcd 11959 gcddiv 11961 bezoutr1 11975 lcmgcd 12019 nn0gcdsq 12141 crth 12165 pythagtriplem1 12206 pcqmul 12244 4sqlem4a 12330 4sqlem4 12331 idmhm 12678 xmetxp 13222 xmetxpbl 13223 txmetcnp 13233 divcnap 13270 rescncf 13283 relogoprlem 13504 lgsdir2 13649 |
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