Theorem oveq 5549

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 5208	. 2 |- ( F = G -> ( F ` <. A , B >. ) = ( G ` <. A , B >. ) )
2		df-ov 5546	. 2 |- ( A F B ) = ( F ` <. A , B >. )
3		df-ov 5546	. 2 |- ( A G B ) = ( G ` <. A , B >. )
4	1, 2, 3	3eqtr4g 2139	1 |- ( F = G -> ( A F B ) = ( A G B ) )

Syntax hints:   -> wi 4   = wceq 1285   <.cop 3409   ` cfv 4932  (class class class)co 5543

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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-uni 3610  df-br 3794  df-iota 4897  df-fv 4940  df-ov 5546

This theorem is referenced by:  oveqi  5556  oveqd  5560  ovmpt2df  5663  ovmpt2dv2  5665