Theorem oveq 6034

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

Step	Hyp	Ref	Expression
1		fveq1 5647	. 2 |- ( F = G -> ( F ` <. A , B >. ) = ( G ` <. A , B >. ) )
2		df-ov 6031	. 2 |- ( A F B ) = ( F ` <. A , B >. )
3		df-ov 6031	. 2 |- ( A G B ) = ( G ` <. A , B >. )
4	1, 2, 3	3eqtr4g 2289	1 |- ( F = G -> ( A F B ) = ( A G B ) )

Syntax hints:   -> wi 4   = wceq 1398   <.cop 3676   ` cfv 5333  (class class class)co 6028

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-uni 3899  df-br 4094  df-iota 5293  df-fv 5341  df-ov 6031

This theorem is referenced by:  oveqi  6041  oveqd  6045  ovmpodf  6163  ovmpodv2  6165  mapxpen  7077  ismgm  13520  mgmsscl  13524  issgrp  13566  ismnddef  13581  grpissubg  13861  isrng  14028  islmod  14387  lmodfopne  14422  ispsmet  15134  ismet  15155  isxmet  15156