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Theorem oveqd 5870
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 5859 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
31, 2syl 14 1 (𝜑 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  (class class class)co 5853
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856
This theorem is referenced by:  oveq123d  5874  oveqdr  5881  csbov12g  5892  ovmpodxf  5978  oprssov  5994  ofeq  6063  fnmpoovd  6194  seqeq2  10405  plusffvalg  12616  mgm1  12624  grpidvalg  12627  grpidd  12637  sgrp1  12651  ismndd  12673  mnd1  12679  ismhm  12685  issubm  12695  isgrp  12714  isgrpd2e  12726  grpidd2  12744  grpinvfvalg  12745  blfvalps  13179
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