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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 5884 |
. 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 2740 df-un 3134 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-iota 5179 df-fv 5225 df-ov 5878 |
This theorem is referenced by: oveq123i 5889 1lt2nq 7405 halfnqq 7409 caucvgprprlemnbj 7692 caucvgprprlemaddq 7707 m1p1sr 7759 m1m1sr 7760 axi2m1 7874 negdii 8241 3t3e9 9076 8th4div3 9138 halfpm6th 9139 numma 9427 decmul10add 9452 4t3lem 9480 9t11e99 9513 halfthird 9526 5recm6rec 9527 fz0to3un2pr 10123 sqdivapi 10604 sq4e2t8 10618 i4 10623 binom2i 10629 facp1 10710 fac2 10711 fac3 10712 fac4 10713 4bc2eq6 10754 cji 10911 fsumadd 11414 fsumsplitf 11416 fsumsplitsnun 11427 0.999... 11529 fprodmul 11599 fprodsplitf 11640 ef01bndlem 11764 cos2bnd 11768 3dvds2dec 11871 flodddiv4 11939 nn0gcdsq 12200 pythagtriplem16 12279 cnmpt2res 13800 txmetcnp 14021 dveflem 14190 efhalfpi 14223 efipi 14225 sin2pi 14227 ef2pi 14229 sincosq3sgn 14252 sincosq4sgn 14253 sinq34lt0t 14255 sincos4thpi 14264 tan4thpi 14265 sincos6thpi 14266 sincos3rdpi 14267 pigt3 14268 lgsdi 14441 2lgsoddprmlem3c 14460 2lgsoddprmlem3d 14461 ex-exp 14482 ex-fac 14483 ex-bc 14484 |
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