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Theorem bcxmaslem1 11527
Description: Lemma for bcxmas 11528. (Contributed by Paul Chapman, 18-May-2007.)
Assertion
Ref Expression
bcxmaslem1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )

Proof of Theorem bcxmaslem1
StepHypRef Expression
1 oveq2 5903 . 2  |-  ( A  =  B  ->  ( N  +  A )  =  ( N  +  B ) )
2 id 19 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2oveq12d 5913 1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1364  (class class class)co 5895    + caddc 7843    _C cbc 10758
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5898
This theorem is referenced by:  bcxmas  11528
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