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Theorem oveqan12d 5474
Description: Equality deduction for operation value. (Contributed by NM, 10-Aug-1995.)
Hypotheses
Ref Expression
oveq1d.1 (φA = B)
opreqan12i.2 (ψ𝐶 = 𝐷)
Assertion
Ref Expression
oveqan12d ((φ ψ) → (A𝐹𝐶) = (B𝐹𝐷))

Proof of Theorem oveqan12d
StepHypRef Expression
1 oveq1d.1 . 2 (φA = B)
2 opreqan12i.2 . 2 (ψ𝐶 = 𝐷)
3 oveq12 5464 . 2 ((A = B 𝐶 = 𝐷) → (A𝐹𝐶) = (B𝐹𝐷))
41, 2, 3syl2an 273 1 ((φ ψ) → (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-bndl 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:  oveqan12rd  5475  offval  5661  offval3  5703  ecovdi  6153  ecovidi  6154  distrpig  6317  addcmpblnq  6351  addpipqqs  6354  mulpipq  6356  addcomnqg  6365  addcmpblnq0  6426  distrnq0  6442  recexprlem1ssl  6605  recexprlem1ssu  6606  1idsr  6696  addcnsrec  6739  mulcnsrec  6740  mulid1  6822  mulsub  7194  mulsub2  7195  muleqadd  7431  divmuldivap  7470  addltmul  7938  fzsubel  8693  fzoval  8775  mulexp  8948  sqdivap  8972  crim  9086  readd  9097  remullem  9099  imadd  9105  cjadd  9112  cjreim  9131
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