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Theorem oveqi 5831
 Description: Equality inference for operation value. (Contributed by NM, 24-Nov-2007.)
Hypothesis
Ref Expression
oveq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
oveqi (𝐶𝐴𝐷) = (𝐶𝐵𝐷)

Proof of Theorem oveqi
StepHypRef Expression
1 oveq1i.1 . 2 𝐴 = 𝐵
2 oveq 5824 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
31, 2ax-mp 5 1 (𝐶𝐴𝐷) = (𝐶𝐵𝐷)
 Colors of variables: wff set class Syntax hints:   = wceq 1335  (class class class)co 5818 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-uni 3773  df-br 3966  df-iota 5132  df-fv 5175  df-ov 5821 This theorem is referenced by:  oveq123i  5832  iseqvalcbv  10338  blres  12794  cncfmet  12939
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