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Theorem oveqan12d 5559
Description: Equality deduction for operation value. (Contributed by NM, 10-Aug-1995.)
Hypotheses
Ref Expression
oveq1d.1  |-  ( ph  ->  A  =  B )
opreqan12i.2  |-  ( ps 
->  C  =  D
)
Assertion
Ref Expression
oveqan12d  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )

Proof of Theorem oveqan12d
StepHypRef Expression
1 oveq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 opreqan12i.2 . 2  |-  ( ps 
->  C  =  D
)
3 oveq12 5549 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A F C )  =  ( B F D ) )
41, 2, 3syl2an 277 1  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    = wceq 1259  (class class class)co 5540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543
This theorem is referenced by:  oveqan12rd  5560  offval  5747  offval3  5789  ecovdi  6248  ecovidi  6249  distrpig  6489  addcmpblnq  6523  addpipqqs  6526  mulpipq  6528  addcomnqg  6537  addcmpblnq0  6599  distrnq0  6615  recexprlem1ssl  6789  recexprlem1ssu  6790  1idsr  6911  addcnsrec  6976  mulcnsrec  6977  mulid1  7082  mulsub  7470  mulsub2  7471  muleqadd  7723  divmuldivap  7763  addltmul  8218  fzsubel  9025  fzoval  9107  iseqid3  9409  mulexp  9459  sqdivap  9484  crim  9686  readd  9697  remullem  9699  imadd  9705  cjadd  9712  cjreim  9731  sqrtmul  9862  sqabsadd  9882  sqabssub  9883  absmul  9896  abs2dif  9933  dvds2ln  10140
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