Theorem oveqi 5901

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 5894	. 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 1363  (class class class)co 5888

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-rex 2471  df-uni 3822  df-br 4016  df-iota 5190  df-fv 5236  df-ov 5891

This theorem is referenced by:  oveq123i  5902  iseqvalcbv  10471  imasplusg  12747  mndprop  12864  issubm  12885  grpprop  12916  ablprop  13134  ringprop  13292  blres  14230  cncfmet  14375