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Theorem oveqan12rd 6103
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 6102 . 2  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )
43ancoms 441 1  |-  ( ( ps  /\  ph )  ->  ( A F C )  =  ( B F D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    = wceq 1653  (class class class)co 6083
This theorem is referenced by:  addpipq  8816  mulgt0sr  8982  mulcnsr  9013  mulresr  9016  recdiv  9722  revccat  11800  rlimdiv  12441  caucvg  12474  ismhm  14742  xrsdsval  16744  ucnval  18309  volcn  19500  dvres2lem  19799  dvid  19806  c1lip3  19885  mpfrcl  19941  taylthlem1  20291  abelthlem9  20358  nonbooli  23155  0cnop  23484  0cnfn  23485  idcnop  23486  brbtwn2  25846  ftc1anc  26290  rmydioph  27087  expdiophlem2  27095  matval  27444
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086
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