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Theorem oveqan12rd 5878
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 5877 . 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 1623  (class class class)co 5858
This theorem is referenced by:  addpipq  8561  mulgt0sr  8727  mulcnsr  8758  mulresr  8761  recdiv  9466  revccat  11484  rlimdiv  12119  caucvg  12151  ismhm  14417  xrsdsval  16415  volcn  18961  dvres2lem  19260  dvid  19267  c1lip3  19346  mpfrcl  19402  taylthlem1  19752  abelthlem9  19816  nonbooli  22230  0cnop  22559  0cnfn  22560  idcnop  22561  brbtwn2  24533  isfuna  25834  idfisf  25841  rmydioph  27107  expdiophlem2  27115  matval  27465
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861
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