ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  oveqd Unicode version

Theorem oveqd 5797
Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006.)
Hypothesis
Ref Expression
oveq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
oveqd  |-  ( ph  ->  ( C A D )  =  ( C B D ) )

Proof of Theorem oveqd
StepHypRef Expression
1 oveq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 oveq 5786 . 2  |-  ( A  =  B  ->  ( C A D )  =  ( C B D ) )
31, 2syl 14 1  |-  ( ph  ->  ( C A D )  =  ( C B D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332  (class class class)co 5780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-uni 3743  df-br 3936  df-iota 5094  df-fv 5137  df-ov 5783
This theorem is referenced by:  oveq123d  5801  csbov12g  5816  ovmpodxf  5902  oprssov  5918  ofeq  5990  fnmpoovd  6118  seqeq2  10251  blfvalps  12586
  Copyright terms: Public domain W3C validator