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Theorem oveqan12rd 6060
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 6059 . 2  |-  ( (
ph  /\  ps )  ->  ( A F C )  =  ( B F D ) )
43ancoms 440 1  |-  ( ( ps  /\  ph )  ->  ( A F C )  =  ( B F D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    = wceq 1649  (class class class)co 6040
This theorem is referenced by:  addpipq  8770  mulgt0sr  8936  mulcnsr  8967  mulresr  8970  recdiv  9676  revccat  11753  rlimdiv  12394  caucvg  12427  ismhm  14695  xrsdsval  16697  ucnval  18260  volcn  19451  dvres2lem  19750  dvid  19757  c1lip3  19836  mpfrcl  19892  taylthlem1  20242  abelthlem9  20309  nonbooli  23106  0cnop  23435  0cnfn  23436  idcnop  23437  brbtwn2  25748  rmydioph  26975  expdiophlem2  26983  matval  27333
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421  df-ov 6043
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