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Theorem oveq12 5464
Description: Equality theorem for operation value. (Contributed by NM, 16-Jul-1995.)
Assertion
Ref Expression
oveq12 ((A = B 𝐶 = 𝐷) → (A𝐹𝐶) = (B𝐹𝐷))

Proof of Theorem oveq12
StepHypRef Expression
1 oveq1 5462 . 2 (A = B → (A𝐹𝐶) = (B𝐹𝐶))
2 oveq2 5463 . 2 (𝐶 = 𝐷 → (B𝐹𝐶) = (B𝐹𝐷))
31, 2sylan9eq 2089 1 ((A = B 𝐶 = 𝐷) → (A𝐹𝐶) = (B𝐹𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242  (class class class)co 5455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458
This theorem is referenced by:  oveq12i  5467  oveq12d  5473  oveqan12d  5474  sprmpt2  5798  ecopoveq  6137  ecopovtrn  6139  ecopovtrng  6142  th3qlem1  6144  th3qlem2  6145  mulcmpblnq  6352  addpipqqs  6354  ordpipqqs  6358  enq0breq  6418  mulcmpblnq0  6426  nqpnq0nq  6435  nqnq0a  6436  nqnq0m  6437  nq0m0r  6438  nq0a0  6439  distrlem5prl  6561  distrlem5pru  6562  addcmpblnr  6647  ltsrprg  6655  mulgt0sr  6684  add20  7244  cru  7366  qaddcl  8326  qmulcl  8328  fzopth  8674  1exp  8918  reval  9057  absval  9190
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