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Theorem oveqdr 5902
Description: Equality of two operations for any two operands. Useful in proofs using *propd theorems. (Contributed by Mario Carneiro, 29-Jun-2015.)
Hypothesis
Ref Expression
oveqdr.1  |-  ( ph  ->  F  =  G )
Assertion
Ref Expression
oveqdr  |-  ( (
ph  /\  ps )  ->  ( x F y )  =  ( x G y ) )

Proof of Theorem oveqdr
StepHypRef Expression
1 oveqdr.1 . . 3  |-  ( ph  ->  F  =  G )
21oveqd 5891 . 2  |-  ( ph  ->  ( x F y )  =  ( x G y ) )
32adantr 276 1  |-  ( (
ph  /\  ps )  ->  ( x F y )  =  ( x G y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    = wceq 1353  (class class class)co 5874
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-uni 3810  df-br 4004  df-iota 5178  df-fv 5224  df-ov 5877
This theorem is referenced by:  grppropstrg  12849  grpsubpropdg  12928  crngpropd  13171  isringd  13173  ring1  13189  opprring  13202  opprringbg  13203  mulgass3  13207  rngidpropdg  13268  invrpropdg  13271  subrgpropd  13329
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