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Theorem oveqan12rd 5894
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
oveqan12rd  |-  ( ( ps  /\  ph )  ->  ( A F C )  =  ( B F D ) )

Proof of Theorem oveqan12rd
StepHypRef Expression
1 oveq1d.1 . . 3  |-  ( ph  ->  A  =  B )
2 opreqan12i.2 . . 3  |-  ( ps 
->  C  =  D
)
31, 2oveqan12d 5893 . 2  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )
43ancoms 439 1  |-  ( ( ps  /\  ph )  ->  ( A F C )  =  ( B F D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1632  (class class class)co 5874
This theorem is referenced by:  addpipq  8577  mulgt0sr  8743  mulcnsr  8774  mulresr  8777  recdiv  9482  revccat  11500  rlimdiv  12135  caucvg  12167  ismhm  14433  xrsdsval  16431  volcn  18977  dvres2lem  19276  dvid  19283  c1lip3  19362  mpfrcl  19418  taylthlem1  19768  abelthlem9  19832  nonbooli  22246  0cnop  22575  0cnfn  22576  idcnop  22577  brbtwn2  24605  isfuna  25937  idfisf  25944  rmydioph  27210  expdiophlem2  27218  matval  27568
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877
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