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Theorem oveqd 5784
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 5773 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
31, 2syl 14 1 (𝜑 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331  (class class class)co 5767
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770
This theorem is referenced by:  oveq123d  5788  csbov12g  5803  ovmpodxf  5889  oprssov  5905  ofeq  5977  fnmpoovd  6105  seqeq2  10215  blfvalps  12543
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