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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 5862 | . 2 | |
4 | 1, 2, 3 | mp2an 424 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 (class class class)co 5853 |
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 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-iota 5160 df-fv 5206 df-ov 5856 |
This theorem is referenced by: oveq123i 5867 1lt2nq 7368 halfnqq 7372 caucvgprprlemnbj 7655 caucvgprprlemaddq 7670 m1p1sr 7722 m1m1sr 7723 axi2m1 7837 negdii 8203 3t3e9 9035 8th4div3 9097 halfpm6th 9098 numma 9386 decmul10add 9411 4t3lem 9439 9t11e99 9472 halfthird 9485 5recm6rec 9486 fz0to3un2pr 10079 sqdivapi 10559 sq4e2t8 10573 i4 10578 binom2i 10584 facp1 10664 fac2 10665 fac3 10666 fac4 10667 4bc2eq6 10708 cji 10866 fsumadd 11369 fsumsplitf 11371 fsumsplitsnun 11382 0.999... 11484 fprodmul 11554 fprodsplitf 11595 ef01bndlem 11719 cos2bnd 11723 3dvds2dec 11825 flodddiv4 11893 nn0gcdsq 12154 pythagtriplem16 12233 cnmpt2res 13091 txmetcnp 13312 dveflem 13481 efhalfpi 13514 efipi 13516 sin2pi 13518 ef2pi 13520 sincosq3sgn 13543 sincosq4sgn 13544 sinq34lt0t 13546 sincos4thpi 13555 tan4thpi 13556 sincos6thpi 13557 sincos3rdpi 13558 pigt3 13559 lgsdi 13732 ex-exp 13762 ex-fac 13763 ex-bc 13764 |
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