Theorem oveqi 6063

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 6056	. 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 6050

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 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rex 2526  df-uni 3915  df-br 4110  df-iota 5312  df-fv 5360  df-ov 6053

This theorem is referenced by:  oveq123i  6064  fvmpopr2d  6190  iseqvalcbv  10821  imasplusg  13521  mndprop  13654  issubm  13685  grpprop  13731  ablprop  14014  ringprop  14184  blres  15299  cncfmet  15457  clwwlknon2  16429