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Theorem oveqd 5472
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 5461 . 2 (A = B → (𝐶A𝐷) = (𝐶B𝐷))
31, 2syl 14 1 (φ → (𝐶A𝐷) = (𝐶B𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  (class class class)co 5455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458
This theorem is referenced by:  oveq123d  5476  csbov12g  5486  ovmpt2dxf  5568  oprssov  5584  ofeq  5656  iseqeq2  8875
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