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Theorem oveq123i 5864
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 5862 . 2  |-  ( A F B )  =  ( C F D )
4 oveq123i.3 . . 3  |-  F  =  G
54oveqi 5863 . 2  |-  ( C F D )  =  ( C G D )
63, 5eqtri 2191 1  |-  ( A F B )  =  ( C G D )
Colors of variables: wff set class
Syntax hints:    = wceq 1348  (class class class)co 5850
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-3an 975  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-v 2732  df-un 3125  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3795  df-br 3988  df-iota 5158  df-fv 5204  df-ov 5853
This theorem is referenced by: (None)
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