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Theorem oveq12i 5552
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 5549 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A F C )  =  ( B F D ) )
41, 2, 3mp2an 410 1  |-  ( A F C )  =  ( B F D )
Colors of variables: wff set class
Syntax hints:    = wceq 1259  (class class class)co 5540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543
This theorem is referenced by:  oveq123i  5554  1lt2nq  6562  halfnqq  6566  caucvgprprlemnbj  6849  caucvgprprlemaddq  6864  m1p1sr  6903  m1m1sr  6904  axi2m1  7007  negdii  7358  3t3e9  8140  8th4div3  8201  halfpm6th  8202  numma  8470  decmul10add  8495  4t3lem  8523  9t11e99  8556  sqdivapi  9503  i4  9521  binom2i  9527  facp1  9598  fac2  9599  fac3  9600  fac4  9601  4bc2eq6  9642  cji  9730  3dvds2dec  10177  flodddiv4  10246  ex-fac  10281  ex-bc  10282
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