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Mirrors > Home > ILE Home > Th. List > oveq12 | Unicode version |
Description: Equality theorem for operation value. (Contributed by NM, 16-Jul-1995.) |
Ref | Expression |
---|---|
oveq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5749 | . 2 | |
2 | oveq2 5750 | . 2 | |
3 | 1, 2 | sylan9eq 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 (class class class)co 5742 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: oveq12i 5754 oveq12d 5760 oveqan12d 5761 ecopoveq 6492 ecopovtrn 6494 ecopovtrng 6497 th3qlem1 6499 th3qlem2 6500 mulcmpblnq 7144 addpipqqs 7146 ordpipqqs 7150 enq0breq 7212 mulcmpblnq0 7220 nqpnq0nq 7229 nqnq0a 7230 nqnq0m 7231 nq0m0r 7232 nq0a0 7233 distrlem5prl 7362 distrlem5pru 7363 addcmpblnr 7515 ltsrprg 7523 mulgt0sr 7554 add20 8204 cru 8332 qaddcl 9395 qmulcl 9397 xaddval 9596 xnn0xadd0 9618 fzopth 9809 modqval 10065 seqvalcd 10200 seqovcd 10204 1exp 10290 m1expeven 10308 nn0opthd 10436 faclbnd 10455 faclbnd3 10457 bcn0 10469 reval 10589 absval 10741 clim 11018 fsumparts 11207 dvds2add 11454 dvds2sub 11455 opoe 11519 omoe 11520 opeo 11521 omeo 11522 gcddvds 11579 gcdcl 11582 gcdeq0 11592 gcdneg 11597 gcdaddm 11599 gcdabs 11603 gcddiv 11634 eucalgval2 11661 lcmabs 11684 rpmul 11706 divgcdcoprmex 11710 prmexpb 11756 rpexp 11758 nn0gcdsq 11805 cnmpt2t 12389 cnmpt22f 12391 hmeofvalg 12399 bdmetval 12596 |
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