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Mirrors > Home > ILE Home > Th. List > oveq12i | Unicode version |
Description: Equality inference for operation value. (Contributed by NM, 28-Feb-1995.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
oveq1i.1 | |
oveq12i.2 |
Ref | Expression |
---|---|
oveq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1i.1 | . 2 | |
2 | oveq12i.2 | . 2 | |
3 | oveq12 5776 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 (class class class)co 5767 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: oveq123i 5781 1lt2nq 7207 halfnqq 7211 caucvgprprlemnbj 7494 caucvgprprlemaddq 7509 m1p1sr 7561 m1m1sr 7562 axi2m1 7676 negdii 8039 3t3e9 8870 8th4div3 8932 halfpm6th 8933 numma 9218 decmul10add 9243 4t3lem 9271 9t11e99 9304 halfthird 9317 5recm6rec 9318 sqdivapi 10369 sq4e2t8 10383 i4 10388 binom2i 10394 facp1 10469 fac2 10470 fac3 10471 fac4 10472 4bc2eq6 10513 cji 10667 fsumadd 11168 fsumsplitf 11170 fsumsplitsnun 11181 0.999... 11283 ef01bndlem 11452 cos2bnd 11456 3dvds2dec 11552 flodddiv4 11620 nn0gcdsq 11867 cnmpt2res 12455 txmetcnp 12676 dveflem 12844 efhalfpi 12869 efipi 12871 sin2pi 12873 ef2pi 12875 sincosq3sgn 12898 sincosq4sgn 12899 sinq34lt0t 12901 sincos4thpi 12910 tan4thpi 12911 sincos6thpi 12912 sincos3rdpi 12913 pigt3 12914 ex-exp 12928 ex-fac 12929 ex-bc 12930 |
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