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Theorem oveq123d 5795
 Description: Equality deduction for operation value. (Contributed by FL, 22-Dec-2008.)
Hypotheses
Ref Expression
oveq123d.1 (𝜑𝐹 = 𝐺)
oveq123d.2 (𝜑𝐴 = 𝐵)
oveq123d.3 (𝜑𝐶 = 𝐷)
Assertion
Ref Expression
oveq123d (𝜑 → (𝐴𝐹𝐶) = (𝐵𝐺𝐷))

Proof of Theorem oveq123d
StepHypRef Expression
1 oveq123d.1 . . 3 (𝜑𝐹 = 𝐺)
21oveqd 5791 . 2 (𝜑 → (𝐴𝐹𝐶) = (𝐴𝐺𝐶))
3 oveq123d.2 . . 3 (𝜑𝐴 = 𝐵)
4 oveq123d.3 . . 3 (𝜑𝐶 = 𝐷)
53, 4oveq12d 5792 . 2 (𝜑 → (𝐴𝐺𝐶) = (𝐵𝐺𝐷))
62, 5eqtrd 2172 1 (𝜑 → (𝐴𝐹𝐶) = (𝐵𝐺𝐷))
 Colors of variables: wff set class Syntax hints:   → wi 4   = 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:  csbov123g  5809
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