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Theorem oveq 6087
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 5727 . 2  |-  ( F  =  G  ->  ( F `  <. A ,  B >. )  =  ( G `  <. A ,  B >. ) )
2 df-ov 6084 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
3 df-ov 6084 . 2  |-  ( A G B )  =  ( G `  <. A ,  B >. )
41, 2, 33eqtr4g 2493 1  |-  ( F  =  G  ->  ( A F B )  =  ( A G B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   <.cop 3817   ` cfv 5454  (class class class)co 6081
This theorem is referenced by:  oveqi  6094  oveqd  6098  ovmpt2df  6205  ovmpt2dv2  6207  seqomeq12  6711  mapxpen  7273  seqeq2  11327  isga  15068  islmod  15954  ispsmet  18335  ismet  18353  isxmet  18354  ishtpy  18997  isphtpy  19006  isgrpo  21784  gidval  21801  grpoinvfval  21812  isablo  21871  isass  21904  isexid  21905  elghomlem1  21949  iscom2  22000  vci  22027  isvclem  22056  isnvlem  22089  isphg  22318  ofceq  24480  cvmlift2lem13  25002  relexp0  25129  relexpsucr  25130  ismtyval  26509  mamuval  27421  mdetleib  27465
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-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-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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