Theorem oveq12i 5555

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	⊢ (𝐴𝐹𝐶) = (𝐵𝐹𝐷)

Proof of Theorem oveq12i

Step	Hyp	Ref	Expression
1		oveq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		oveq12i.2	. 2 ⊢ 𝐶 = 𝐷
3		oveq12 5552	. 2 ⊢ ((𝐴 = 𝐵 ∧ 𝐶 = 𝐷) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷))
4	1, 2, 3	mp2an 417	1 ⊢ (𝐴𝐹𝐶) = (𝐵𝐹𝐷)

Syntax hints:   = wceq 1285  (class class class)co 5543

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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-br 3794  df-iota 4897  df-fv 4940  df-ov 5546

This theorem is referenced by:  oveq123i  5557  1lt2nq  6658  halfnqq  6662  caucvgprprlemnbj  6945  caucvgprprlemaddq  6960  m1p1sr  6999  m1m1sr  7000  axi2m1  7103  negdii  7459  3t3e9  8256  8th4div3  8317  halfpm6th  8318  numma  8601  decmul10add  8626  4t3lem  8654  9t11e99  8687  sqdivapi  9656  i4  9674  binom2i  9680  facp1  9754  fac2  9755  fac3  9756  fac4  9757  4bc2eq6  9798  cji  9927  3dvds2dec  10410  flodddiv4  10478  ex-fac  10716  ex-bc  10717