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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 |
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opreqan12i.2 |
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Ref | Expression |
---|---|
oveqan12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1d.1 |
. 2
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2 | opreqan12i.2 |
. 2
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3 | oveq12 5735 |
. 2
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4 | 1, 2, 3 | syl2an 285 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-rex 2394 df-v 2657 df-un 3039 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-br 3894 df-iota 5044 df-fv 5087 df-ov 5729 |
This theorem is referenced by: oveqan12rd 5746 offval 5941 offval3 5984 ecovdi 6492 ecovidi 6493 distrpig 7083 addcmpblnq 7117 addpipqqs 7120 mulpipq 7122 addcomnqg 7131 addcmpblnq0 7193 distrnq0 7209 recexprlem1ssl 7383 recexprlem1ssu 7384 1idsr 7505 addcnsrec 7571 mulcnsrec 7572 mulid1 7681 mulsub 8076 mulsub2 8077 muleqadd 8336 divmuldivap 8379 div2subap 8503 addltmul 8854 xnegdi 9538 fzsubel 9727 fzoval 9812 mulexp 10219 sqdivap 10244 crim 10517 readd 10528 remullem 10530 imadd 10536 cjadd 10543 cjreim 10562 sqrtmul 10693 sqabsadd 10713 sqabssub 10714 absmul 10727 abs2dif 10764 binom 11139 sinadd 11288 cosadd 11289 dvds2ln 11368 absmulgcd 11545 gcddiv 11547 bezoutr1 11561 lcmgcd 11599 nn0gcdsq 11717 crth 11739 xmetxp 12490 xmetxpbl 12491 txmetcnp 12501 divcnap 12535 rescncf 12548 |
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