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Theorem bcxmaslem1 11288
Description: Lemma for bcxmas 11289. (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 5789 . 2  |-  ( A  =  B  ->  ( N  +  A )  =  ( N  +  B ) )
2 id 19 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2oveq12d 5799 1  |-  ( A  =  B  ->  (
( N  +  A
)  _C  A )  =  ( ( N  +  B )  _C  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332  (class class class)co 5781    + caddc 7646    _C cbc 10524
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-3an 965  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-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-iota 5095  df-fv 5138  df-ov 5784
This theorem is referenced by:  bcxmas  11289
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