Theorem oveqi 6020

Description: Equality inference for operation value. (Contributed by NM, 24-Nov-2007.)

Hypothesis

Ref	Expression
oveq1i.1	|- A = B

Assertion

Ref	Expression
oveqi	|- ( C A D ) = ( C B D )

Proof of Theorem oveqi

Step	Hyp	Ref	Expression
1		oveq1i.1	. 2 |- A = B
2		oveq 6013	. 2 |- ( A = B -> ( C A D ) = ( C B D ) )
3	1, 2	ax-mp 5	1 |- ( C A D ) = ( C B D )

Syntax hints:   = wceq 1395  (class class class)co 6007

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-uni 3889  df-br 4084  df-iota 5278  df-fv 5326  df-ov 6010

This theorem is referenced by:  oveq123i  6021  fvmpopr2d  6147  iseqvalcbv  10689  imasplusg  13349  mndprop  13482  issubm  13513  grpprop  13559  ablprop  13842  ringprop  14011  blres  15116  cncfmet  15274