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Theorem oveq12i 5752
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 5749 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A F C )  =  ( B F D ) )
41, 2, 3mp2an 420 1  |-  ( A F C )  =  ( B F D )
Colors of variables: wff set class
Syntax hints:    = wceq 1314  (class class class)co 5740
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099  df-ov 5743
This theorem is referenced by:  oveq123i  5754  1lt2nq  7178  halfnqq  7182  caucvgprprlemnbj  7465  caucvgprprlemaddq  7480  m1p1sr  7532  m1m1sr  7533  axi2m1  7647  negdii  8010  3t3e9  8831  8th4div3  8893  halfpm6th  8894  numma  9179  decmul10add  9204  4t3lem  9232  9t11e99  9265  sqdivapi  10327  sq4e2t8  10341  i4  10346  binom2i  10352  facp1  10427  fac2  10428  fac3  10429  fac4  10430  4bc2eq6  10471  cji  10625  fsumadd  11126  fsumsplitf  11128  fsumsplitsnun  11139  0.999...  11241  ef01bndlem  11373  cos2bnd  11377  3dvds2dec  11470  flodddiv4  11538  nn0gcdsq  11784  cnmpt2res  12372  txmetcnp  12593  dveflem  12761  ex-exp  12773  ex-fac  12774  ex-bc  12775
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