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Theorem oveq12i 5625
Description: Equality inference for operation value. (Contributed by NM, 28-Feb-1995.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Hypotheses
Ref Expression
oveq1i.1  |-  A  =  B
oveq12i.2  |-  C  =  D
Assertion
Ref Expression
oveq12i  |-  ( A F C )  =  ( B F D )

Proof of Theorem oveq12i
StepHypRef Expression
1 oveq1i.1 . 2  |-  A  =  B
2 oveq12i.2 . 2  |-  C  =  D
3 oveq12 5622 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A F C )  =  ( B F D ) )
41, 2, 3mp2an 417 1  |-  ( A F C )  =  ( B F D )
Colors of variables: wff set class
Syntax hints:    = wceq 1287  (class class class)co 5613
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3637  df-br 3821  df-iota 4946  df-fv 4989  df-ov 5616
This theorem is referenced by:  oveq123i  5627  1lt2nq  6909  halfnqq  6913  caucvgprprlemnbj  7196  caucvgprprlemaddq  7211  m1p1sr  7250  m1m1sr  7251  axi2m1  7354  negdii  7710  3t3e9  8507  8th4div3  8568  halfpm6th  8569  numma  8852  decmul10add  8877  4t3lem  8905  9t11e99  8938  sqdivapi  9937  i4  9955  binom2i  9961  facp1  10035  fac2  10036  fac3  10037  fac4  10038  4bc2eq6  10079  cji  10232  3dvds2dec  10748  flodddiv4  10816  nn0gcdsq  11060  ex-fac  11100  ex-bc  11101
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