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Theorem oveq 5619
Description: Equality theorem for operation value. (Contributed by NM, 28-Feb-1995.)
Assertion
Ref Expression
oveq  |-  ( F  =  G  ->  ( A F B )  =  ( A G B ) )

Proof of Theorem oveq
StepHypRef Expression
1 fveq1 5267 . 2  |-  ( F  =  G  ->  ( F `  <. A ,  B >. )  =  ( G `  <. A ,  B >. ) )
2 df-ov 5616 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
3 df-ov 5616 . 2  |-  ( A G B )  =  ( G `  <. A ,  B >. )
41, 2, 33eqtr4g 2142 1  |-  ( F  =  G  ->  ( A F B )  =  ( A G B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   <.cop 3434   ` cfv 4981  (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-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-uni 3637  df-br 3821  df-iota 4946  df-fv 4989  df-ov 5616
This theorem is referenced by:  oveqi  5626  oveqd  5630  ovmpt2df  5733  ovmpt2dv2  5735  mapxpen  6516
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