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Theorem oveqd 5843
Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006.)
Hypothesis
Ref Expression
oveq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
oveqd (𝜑 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))

Proof of Theorem oveqd
StepHypRef Expression
1 oveq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 oveq 5832 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
31, 2syl 14 1 (𝜑 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1335  (class class class)co 5826
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 3775  df-br 3968  df-iota 5137  df-fv 5180  df-ov 5829
This theorem is referenced by:  oveq123d  5847  csbov12g  5862  ovmpodxf  5948  oprssov  5964  ofeq  6036  fnmpoovd  6164  seqeq2  10357  blfvalps  12855
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