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Theorem oveqan12rd 6110
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 6109 . 2  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )
43ancoms 450 1  |-  ( ( ps  /\  ph )  ->  ( A F C )  =  ( B F D ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    = wceq 1364  (class class class)co 6090
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-rex 2719  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-uni 4089  df-br 4290  df-iota 5378  df-fv 5423  df-ov 6093
This theorem is referenced by:  addpipq  9102  mulgt0sr  9268  mulcnsr  9299  mulresr  9302  recdiv  10033  revccat  12402  rlimdiv  13119  caucvg  13152  ismhm  15462  xrsdsval  17757  matval  18211  ucnval  19752  volcn  20986  dvres2lem  21285  dvid  21292  c1lip3  21371  mpfrcl  21428  taylthlem1  21781  abelthlem9  21848  brbtwn2  23070  nonbooli  24973  0cnop  25302  0cnfn  25303  idcnop  25304  ftc1anc  28384  rmydioph  29272  expdiophlem2  29280
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