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Theorem oveqan12rd 5794
 Description: Equality deduction for operation value. (Contributed by NM, 10-Aug-1995.)
Hypotheses
Ref Expression
oveq1d.1 (𝜑𝐴 = 𝐵)
opreqan12i.2 (𝜓𝐶 = 𝐷)
Assertion
Ref Expression
oveqan12rd ((𝜓𝜑) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷))

Proof of Theorem oveqan12rd
StepHypRef Expression
1 oveq1d.1 . . 3 (𝜑𝐴 = 𝐵)
2 opreqan12i.2 . . 3 (𝜓𝐶 = 𝐷)
31, 2oveqan12d 5793 . 2 ((𝜑𝜓) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷))
43ancoms 266 1 ((𝜓𝜑) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   = wceq 1331  (class class class)co 5774 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 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777 This theorem is referenced by:  mulresr  7653  recdivap  8485  divgcdcoprm0  11788  dvid  12840
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