Theorem oveq12i 5544

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

Step	Hyp	Ref	Expression
1		oveq1i.1	. 2 |- A = B
2		oveq12i.2	. 2 |- C = D
3		oveq12 5541	. 2 |- ( ( A = B /\ C = D ) -> ( A F C ) = ( B F D ) )
4	1, 2, 3	mp2an 416	1 |- ( A F C ) = ( B F D )

Syntax hints:   = wceq 1284  (class class class)co 5532

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-uni 3602  df-br 3786  df-iota 4887  df-fv 4930  df-ov 5535

This theorem is referenced by:  oveq123i  5546  1lt2nq  6596  halfnqq  6600  caucvgprprlemnbj  6883  caucvgprprlemaddq  6898  m1p1sr  6937  m1m1sr  6938  axi2m1  7041  negdii  7392  3t3e9  8189  8th4div3  8250  halfpm6th  8251  numma  8520  decmul10add  8545  4t3lem  8573  9t11e99  8606  sqdivapi  9559  i4  9577  binom2i  9583  facp1  9657  fac2  9658  fac3  9659  fac4  9660  4bc2eq6  9701  cji  9789  3dvds2dec  10265  flodddiv4  10334  ex-fac  10565  ex-bc  10566