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Theorem oveq123i 6095
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 6093 . 2  |-  ( A F B )  =  ( C F D )
4 oveq123i.3 . . 3  |-  F  =  G
54oveqi 6094 . 2  |-  ( C F D )  =  ( C G D )
63, 5eqtri 2456 1  |-  ( A F B )  =  ( C G D )
Colors of variables: wff set class
Syntax hints:    = wceq 1652  (class class class)co 6081
This theorem is referenced by:  mendvscafval  27475  cytpval  27505
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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