Theorem oveqi 6071

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 6064	. 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 1398  (class class class)co 6058

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 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rex 2528  df-uni 3920  df-br 4115  df-iota 5317  df-fv 5365  df-ov 6061

This theorem is referenced by:  oveq123i  6072  fvmpopr2d  6198  iseqvalcbv  10845  imasplusg  13572  mndprop  13702  issubm  13727  grpprop  13773  ablprop  14050  ringprop  14283  blres  15425  cncfmet  15583  clwwlknon2  16555