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Theorem oveq 5773
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 5413 . 2  |-  ( F  =  G  ->  ( F `  <. A ,  B >. )  =  ( G `  <. A ,  B >. ) )
2 df-ov 5770 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
3 df-ov 5770 . 2  |-  ( A G B )  =  ( G `  <. A ,  B >. )
41, 2, 33eqtr4g 2195 1  |-  ( F  =  G  ->  ( A F B )  =  ( A G B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331   <.cop 3525   ` cfv 5118  (class class class)co 5767
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770
This theorem is referenced by:  oveqi  5780  oveqd  5784  ovmpodf  5895  ovmpodv2  5897  mapxpen  6735  ispsmet  12481  ismet  12502  isxmet  12503
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