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Theorem oveq123i 5627
Description: Equality inference for operation value. (Contributed by FL, 11-Jul-2010.)
Hypotheses
Ref Expression
oveq123i.1  |-  A  =  C
oveq123i.2  |-  B  =  D
oveq123i.3  |-  F  =  G
Assertion
Ref Expression
oveq123i  |-  ( A F B )  =  ( C G D )

Proof of Theorem oveq123i
StepHypRef Expression
1 oveq123i.1 . . 3  |-  A  =  C
2 oveq123i.2 . . 3  |-  B  =  D
31, 2oveq12i 5625 . 2  |-  ( A F B )  =  ( C F D )
4 oveq123i.3 . . 3  |-  F  =  G
54oveqi 5626 . 2  |-  ( C F D )  =  ( C G D )
63, 5eqtri 2105 1  |-  ( A F B )  =  ( C G D )
Colors of variables: wff set class
Syntax hints:    = wceq 1287  (class class class)co 5613
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3637  df-br 3821  df-iota 4946  df-fv 4989  df-ov 5616
This theorem is referenced by: (None)
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