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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 |
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oveq12i.2 |
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Ref | Expression |
---|---|
oveq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1i.1 |
. 2
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2 | oveq12i.2 |
. 2
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3 | oveq12 5881 |
. 2
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4 | 1, 2, 3 | mp2an 426 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 |
This theorem is referenced by: oveq123i 5886 1lt2nq 7402 halfnqq 7406 caucvgprprlemnbj 7689 caucvgprprlemaddq 7704 m1p1sr 7756 m1m1sr 7757 axi2m1 7871 negdii 8237 3t3e9 9072 8th4div3 9134 halfpm6th 9135 numma 9423 decmul10add 9448 4t3lem 9476 9t11e99 9509 halfthird 9522 5recm6rec 9523 fz0to3un2pr 10118 sqdivapi 10598 sq4e2t8 10612 i4 10617 binom2i 10623 facp1 10703 fac2 10704 fac3 10705 fac4 10706 4bc2eq6 10747 cji 10904 fsumadd 11407 fsumsplitf 11409 fsumsplitsnun 11420 0.999... 11522 fprodmul 11592 fprodsplitf 11633 ef01bndlem 11757 cos2bnd 11761 3dvds2dec 11863 flodddiv4 11931 nn0gcdsq 12192 pythagtriplem16 12271 cnmpt2res 13668 txmetcnp 13889 dveflem 14058 efhalfpi 14091 efipi 14093 sin2pi 14095 ef2pi 14097 sincosq3sgn 14120 sincosq4sgn 14121 sinq34lt0t 14123 sincos4thpi 14132 tan4thpi 14133 sincos6thpi 14134 sincos3rdpi 14135 pigt3 14136 lgsdi 14309 ex-exp 14339 ex-fac 14340 ex-bc 14341 |
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